Control Barrier Function papers | Updated: 2026-09-10 00:52 UTC
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Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by high-dimensional nonlinear dynamics, which presents challenges for model-based safety-critical control design. Motivated by the success of reduced-order models in robotics, this paper presents a tutorial on constructive safety-critical control via reduced-order models and control barrier functions (CBFs). To this end, we provide a unified formulation of techniques in the literature that share a common foundation of constructing CBFs for complex systems from CBFs for much simpler systems. Such ideas are illustrated through formal results, simple numerical examples, and case studies of real-world systems to which these techniques have been experimentally applied.
Today’s control engineering problems exhibit an unprecedented complexity, with examples including the reliable integration of renewable energy sources into power grids
Many safety-critical applications of neural networks, such as robotic control, require safety guarantees. This article introduces a method for ensuring the safety of learned models for control using differentiable control barrier functions (dCBFs). dCBFs are end-to-end trainable and guarantee safety. They improve over classical control barrier functions (CBFs), which are usually overly conservative. Our dCBF solution relaxes the CBF definitions by: 1) using environmental dependencies; 2) embedding them into differentiable quadratic programs. These novel safety layers are called a BarrierNet. They can be used in conjunction with any neural network-based controller. They are trained by gradient descent. With BarrierNet, the safety constraints of a neural controller become adaptable to changing environments. We evaluate BarrierNet on the following several problems: 1) robot traffic merging; 2) robot navigation in 2-D and 3-D spaces; 3) end-to-end vision-based autonomous driving in a sim-to-real environment and in physical experiments; 4) demonstrate their effectiveness compared to state-of-the-art approaches.
Balancing safety and performance is one of the predominant challenges in modern control system design. Moreover, it is crucial to robustly ensure safety without inducing unnecessary conservativeness that degrades performance. In this work, we present a constructive approach for safety-critical control synthesis via control barrier functions (CBFs). By filtering a hand-designed controller via a CBF, we are able to attain performant behavior while providing rigorous guarantees of safety. In the face of disturbances, robust safety and performance are simultaneously achieved through the notion of input-to-state safety (ISSf). We take a tutorial approach by developing the CBF-design methodology in parallel with an inverted pendulum example, making the challenges and sensitivities in the design process concrete. To establish the capability of the proposed approach, we consider the practical setting of safety-critical design via CBFs for a connected automated vehicle (CAV) in the form of a class-8 truck without a trailer. Through experimentation, we see the impact of unmodeled disturbances in the truck’s actuation system on the safety guarantees provided by CBFs. We characterize these disturbances and using ISSf, produce a robust controller that achieves safety without conceding performance. We evaluate our design both in simulation, and for the first time on an automotive system, experimentally.
Reinforcement Learning (RL) has been shown to be effective in many scenarios. However, it typically requires the exploration of a sufficiently large number of state-action pairs, some of which may be unsafe. Consequently, its application to safety-critical systems remains a challenge. An increasingly common approach to address safety involves the addition of a safety layer that projects the RL actions onto a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the safety layer to improve the learning performance. In this letter, we frame safety as a differentiable robust-control-barrier-function layer in a model-based RL framework. Moreover, we also propose an approach to modularly learn the underlying reward-driven task, independent of safety constraints. We demonstrate that this approach both ensures safety and effectively guides exploration during training in a range of experiments, including zero-shot transfer when the reward is learned in a constraint-agnostic fashion.
Obstacle avoidance between polytopes is a chal-lenging topic for optimal control and optimization-based tra-jectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simpli-fication of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control barrier function (DCBF) constraints and we propose a novel optimization formulation with dual variables based on DCBFs to generate a collision-free dynamically-feasible trajectory. The proposed optimization formulation has lower computational complexity compared to existing work and can be used as a fast online algorithm for control and planning for general nonlinear dynamical systems. We validate our algorithm on different robot shapes using numerical simulations with a kinematic bicycle model, resulting in successful navigation through maze environments with polytopic obstacles.
This article addresses the safety-critical containment maneuvering of multiple underactuated autonomous surface vehicles (ASVs) in the presence of multiple stationary/moving obstacles. In a complex marine environment, every ASV suffers from model uncertainties, external disturbances, and input constraints. A safety-critical control method is proposed for achieving a collision-free containment formation. Specifically, a fixed-time extended state observer is employed for estimating the model uncertainties and external disturbances. By estimating lumped disturbances in fixed time, nominal containment maneuvering control laws are designed in an Earth-fixed reference frame. Input-to-state safe control barrier functions (ISSf-CBFs) are constructed for mapping safety constraints on states to constraints on control inputs. A distributed quadratic optimization problem with the norm of control inputs as the objective function and ISSf-CBFs as constraints is formulated. A recurrent neural network-based neurodynamic optimization approach is adopted to solve the quadratic optimization problem for computing the forces and moments within the safety and input constraints in real time. It is proven that the error signals in the closed-loop control system are uniformly ultimately bounded and the multi-ASVs system is guaranteed for input-to-state safety. Simulation results are elaborated to substantiate the effectiveness of the proposed safety-critical control method for ASVs based on neurodynamic optimization with control barrier functions.
We approach the problem of stabilizing a dynamical system while optimizing a cost and satisfying safety constraints and control limitations. For (nonlinear) affine control systems and quadratic costs, it has been shown that control barrier functions (CBFs) guaranteeing safety and control Lyapunov functions (CLFs) enforcing convergence can be used to (conservatively) reduce the optimal control problem to a sequence of quadratic programs (QPs). Existing works in this category have two main limitations. First, with one exception, they are based on the assumption that the relative degree of the system with respect to a function enforcing a safety constraint is one. Second, the QPs can easily become infeasible, in particular for problems with many safety constraints and tight control limitations. We propose high-order CBFs (HOCBFs), which can accommodate systems of arbitrary relative degrees. For each safety constraint, by using Lyapunov-like conditions, we construct a set of controls that renders the intersection of a set of sets forward invariant, which implies the satisfaction of the original constraint. We formulate optimal control problems with constraints given by HOCBF and CLF, and propose two methods—the penalty method and the parameterization method—to address the feasibility problem. Finally, we show how our methodology can be extended for safe navigation in unknown environments with long-term feasibility. We illustrate the proposed framework on adaptive cruise control and robot control problems.
A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainty. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive controller for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as contraction does not require the system be invertible or in a particular form. The method is tested on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.
Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs). The limitations of these existing approaches are mainly about feasibility and safety. In the existing approaches, the feasibility of the optimization and the system safety cannot be enhanced at the same time theoretically. In this paper, we propose two formulations that unifies CLFs and CBFs under the framework of nonlinear model predictive control (NMPC). In the proposed formulations, safety criteria is commonly formulated as CBF constraints and stability performance is ensured with either a terminal cost function or CLF constraints. Slack variables with relaxing technique are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same. The advantages about feasibility and safety of proposed formulations compared with existing methods are analyzed theoretically and validated with numerical results.
While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive safety filters, which assess if a proposed learning-based control input can lead to constraint violations and modifies it if necessary to ensure safety for all future time steps. The theoretical guarantees of such predictive safety filters rely on the model assumptions and minor deviations can lead to failure of the filter putting the system at risk. This article introduces an auxiliary soft-constrained predictive control problem that is always feasible at each time step and asymptotically stabilizes the feasible set of the original predictive safety filter problem, thereby providing a recovery mechanism in safety–critical situations. This is achieved by a simple constraint tightening in combination with a terminal control barrier function. By extending discrete-time control barrier function theory, we establish that the proposed auxiliary problem provides a “predictive” control barrier function. The resulting algorithm is demonstrated using numerical examples.
The backup control barrier function (CBF) was recently proposed as a tractable formulation that guarantees the feasibility of the CBF quadratic programming (QP) via an implicitly defined control invariant set. The control invariant set is based on a fixed backup policy and evaluated online by forward integrating the dynamics under the backup policy. This paper is intended as a tutorial of the backup CBF approach and a comparative study to some benchmarks. First, the backup CBF approach is presented step by step with the underlying math explained in detail. Second, we prove that the backup CBF always has a relative degree 1 under mild assumptions. Third, the backup CBF approach is compared with benchmarks such as Hamilton Jacobi PDE and Sum-of-Squares on the computation of control invariant sets, which shows that one can obtain a control invariant set close to the maximum control invariant set under a good backup policy for many practical problems.
It has been shown that optimizing quadratic costs while stabilizing affine control systems to desired (sets of) states subject to state and control constraints can be reduced to a sequence of quadratic programs (QPs) by using control barrier functions (CBFs) and control Lyapunov functions (CLFs). In this article, we introduce adaptive CBFs (aCBFs) that can accommodate time-varying control bounds and noise in the system dynamics while also guaranteeing the feasibility of the QPs if the original quadratic cost optimization problem itself is feasible, which is a challenging problem in current approaches. We propose two different types of aCBFs: parameter-adaptive CBF (PACBF) and relaxation-adaptive CBF (RACBF). Central to aCBFs is the introduction of appropriate time-varying functions to modify the definition of a common CBF. These time-varying functions are treated as high-order CBFs with their own auxiliary dynamics, which are stabilized by CLFs. We demonstrate the advantages of using aCBFs over the existing CBF techniques by applying both the PACBF-based method and the RACBF-based method to a cruise control problem with time-varying road conditions and noise in the system dynamics, and compare their relative performance.
To bring complex systems into real world environments in a safe manner, they will have to be robust to uncertainties—both in the environment and the system. This letter investigates the safety of control systems under input disturbances, wherein the disturbances can capture uncertainties in the system. Safety, framed as forward invariance of sets in the state space, is ensured with the framework of control barrier functions (CBFs). Concretely, the definition of input-to-state safety (ISSf) is generalized to allow the synthesis of non-conservative, tunable controllers that are provably safe under varying disturbances. This is achieved by formulating the concept of tunable input-to-state safe control barrier functions (TISSf-CBFs), which guarantee safety for disturbances that vary with state and, therefore, provide less conservative means of accommodating uncertainty. The theoretical results are demonstrated with a simple control system with input disturbance and also applied to design a safe connected cruise controller for a heavy duty truck.
Artificial potential fields (APFs) and their variants have been a staple for collision avoidance of mobile robots and manipulators for almost 40 years. Its model-independent nature, ease of implementation, and real-time performance have played a large role in its continued success over the years. Control barrier functions (CBFs), on the other hand, are a more recent development, commonly used to guarantee safety for nonlinear systems in real-time in the form of a filter on a nominal controller. In this paper, we address the connections between APFs and CBFs. At a theoretic level, we show that given a broad class of APFs, one can construct a CBF that guarantees safety. Additionally, we prove that CBFs obtained from these APFs have additional beneficial properties and can be applied to nonlinear systems. Practically, we compare the performance of APFs and CBFs in the context of obstacle avoidance on simple illustrative examples and for a quadrotor with unknown dynamics, both in simulation and on hardware using onboard sensing.
In this paper, the issue of model uncertainty in safety-critical control is addressed with a data-driven approach. For this purpose, we utilize the structure of an input-ouput linearization controller based on a nominal model along with a Control Barrier Function and Control Lyapunov Function based Quadratic Program (CBF-CLF-QP). Specifically, we propose a novel reinforcement learning framework which learns the model uncertainty present in the CBF and CLF constraints, as well as other control-affine dynamic constraints in the quadratic program. The trained policy is combined with the nominal model-based CBF-CLF-QP, resulting in the Reinforcement Learning-based CBF-CLF-QP (RL-CBF-CLF-QP), which addresses the problem of model uncertainty in the safety constraints. The performance of the proposed method is validated by testing it on an underactuated nonlinear bipedal robot walking on randomly spaced stepping stones with one step preview, obtaining stable and safe walking under model uncertainty.
Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs). We consider the setting of a known nonlinear control affine dynamical system and assume that we have access to safe trajectories generated by an expert — a practical example of such a setting would be a kinematic model of a self-driving vehicle with safe trajectories (e.g., trajectories that avoid collisions with obstacles in the environment) generated by a human driver. We then propose and analyze an optimization based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz smoothness assumptions on the underlying dynamical system. A strength of our approach is that it is agnostic to the parameterization used to represent the CBF, assuming only that the Lipschitz constant of such functions can be efficiently bounded. Furthermore, if the CBF parameterization is convex, then under mild assumptions, so is our learning process. We end with extensive numerical evaluations of our results on both planar and realistic examples, using both random feature and deep neural network parameterizations of the CBF. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.
Control Barrier Functions (CBFs) aim to ensure safety by constraining the control input at each time step so that the system state remains within a desired safe region. This paper presents a framework for CBFs in stochastic systems in the presence of Gaussian process and measurement noise. We first consider the case where the system state is known at each time step, and present reciprocal and zero CBF constructions that guarantee safety with probability 1. We extend our results to high relative degree systems with linear dynamics and affine safety constraints. We then develop CBFs for incomplete state information environments, in which the state must be estimated using sensors that are corrupted by Gaussian noise. We prove that our proposed CBF ensures safety with probability 1 when the state estimate is within a given bound of the true state, which can be achieved using an Extended Kalman Filter when the system is linear or the process and measurement noise are sufficiently small. We propose control policies that combine these CBFs with Control Lyapunov Functions in order to jointly ensure safety and stochastic stability. Our results are validated via numerical study on an adaptive cruise control example.
Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunov-based methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the system’s state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this unified framework to achieve stability and safety in an Adaptive Cruise Control (ACC) simulation.
This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.
This paper extends control barrier functions (CBFs) to high order control barrier functions (HOCBFs) that can be used for high relative degree constraints. The proposed HOCBFs are more general than recently proposed (exponential) HOCBFs. We introduce high order barrier functions (HOBFs), and show that their satisfaction of Lyapunov-like conditions implies the forward invariance of the intersection of a series of sets. We then introduce HOCBF, and show that any control input that satisfies the HOCBF constraint renders the intersection of a series of sets forward invariant. We formulate optimal control problems with constraints given by HOCBF and control Lyapunov functions (CLF), and provide a promising method to address the conflict between HOCBF constraints and control limitations by penalizing the class $\mathcal{K}$ functions. We illustrate the proposed method on an adaptive cruise control problem.
The need for computationally-efficient control methods of dynamical systems under temporal logic tasks has recently become more apparent. Existing methods are computationally demanding and hence often not applicable in practice. Especially with respect to multi-robot systems, these methods do not scale computationally. In this letter, we propose a framework that is based on control barrier functions and signal temporal logic. In particular, time-varying control barrier functions are considered where the temporal properties are used to satisfy signal temporal logic tasks. The resulting controller is given by a switching strategy between a computationally-efficient convex quadratic program and a local feedback control law.
Abstract Quadratic Programming (QP) has been used to combine Control Lyapunov and Control Barrier Functions (CLF and CBF) to design controllers for nonlinear systems with constraints. It has been successfully applied to robotic and automotive systems. The approach could be considered an extension of the CLF-based point-wise minimum norm controller. In this paper we modify the original QP problem in a way that guarantees that V 0 , if the barrier constraint is inactive, as well as local asymptotic stability under the standard (minimal) assumptions on the CLF and CBF. We also remove the assumption that the CBF has uniform relative degree one. The two design parameters of the new QP setup allow us to control how aggressive the resulting control law is when trying to satisfy the two control objectives. The paper presents the controller in a closed form making it unnecessary to solve the QP problem on line and facilitating the analysis. Next, we introduce the concept of Robust-CBF that, when combined with existing ISS-CLFs, produces controllers for constrained nonlinear systems with disturbances. In an example, a nonlinear system is used to illustrate the ease with which the proposed design method handles non-convex constraints and disturbances and to illuminate some tradeoffs.
This letter presents a new notion of input-to-state safe control barrier functions (ISSf-CBFs), which ensure safety of nonlinear dynamical systems under input disturbances. Similar to how safety conditions are specified in terms of forward invariance of a set, input-to-state safety conditions are specified in terms of forward invariance of a slightly larger set. In this context, invariance of the larger set implies that the states stay either inside or very close to the smaller safe set; and this closeness is bounded by the magnitude of the disturbances. The main contribution of the letter is the methodology used for obtaining a valid ISSf-CBF, given a control barrier function. The associated universal control law will also be provided. Towards the end, we will study unified quadratic programs that combine control Lyapunov functions and ISSf-CBFs in order to obtain a single control law that ensures both safety and stability in systems with input disturbances.
—In this paper, we extend the concept of control barrier functions, developed initially for continuous time systems, to the discrete-time domain. We demonstrate safety-critical con- trol for nonlinear discrete-time systems with applications to 3D bipedal robot navigation. Particularly, we mathematically analyze two different formulations of control barrier functions, based on their continuous-time counterparts, and demonstrate how these can be applied to discrete-time systems. We show that in general, the resulting formulation is a nonlinear program in contrast to the quadratic program for continuous-time systems. We show that under certain conditions that the nonlinear program can be formulated as a quadratically constrained quadratic program. Furthermore, using the developed concept of discrete control barrier functions, we present a novel control method to address the problem of navigation of a high-dimensional bipedal robot through environments with moving obstacles that present time-varying safety-critical constraints.
Abstract Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control. The extension of a barrier function to a controlled system results in a control barrier function. This can be thought of as being analogous to how Sontag extended Lyapunov functions to control Lypaunov functions in order to enable controller synthesis for stabilization tasks. A control barrier function enables controller synthesis for safety requirements specified by forward invariance of a set using a Lyapunov-like condition. This paper develops several important extensions to the notion of a control barrier function. The first involves robustness under perturbations to the vector field defining the system. Input-to-State stability conditions are given that provide for forward invariance, when disturbances are present, of a “relaxation” of set rendered invariant without disturbances. A control barrier function can be combined with a control Lyapunov function in a quadratic program to achieve a control objective subject to safety guarantees. The second result of the paper gives conditions for the control law obtained by solving the quadratic program to be Lipschitz continuous and therefore to gives rise to well-defined solutions of the resulting closed-loop system.
Robots navigating under occlusion may enter states from which no admissible input can avoid a dynamic obstacle once it becomes visible. We present OcclusionCBF, a safety filter that extends backup control barrier functions to reachable-occupancy predictions for potentially hidden dynamic obstacles in occluded regions. The method certifies a prescribed backup rollout against collision-inflated occupancy and a verified terminal set, yielding affine constraints for minimally invasive quadratic-program filtering. We establish recursive feasibility of the resulting safety filter, and collision avoidance for every hidden-obstacle motion covered by the occupancy prediction. Randomized benchmarks, MetaUrban simulations, and hardware experiments demonstrate improved task success over reactive and occlusion-aware predictive baselines with millisecond-scale computation.
The autonomous localization of fugitive gas emissions using small Unmanned Aircraft Systems (sUAS) constitutes a fundamentally ill-posed inverse problem. In turbulent atmospheric boundary layers, highly intermittent scalar concentration fields violate the assumptions of classical gradient-based navigation, causing data-driven estimators to suffer from severe noise and spurious local minima. To address these challenges, we introduce an Information-Guided Safe Reinforcement Learning framework evaluated within a custom, GPU-accelerated 3D simulation environment coupling an Eulerian wind solver with a Lagrangian puff dispersion model. We identify a critical vulnerability in deterministic information-seeking planners - a Gramian bias where agents act greedily upon flawed early estimates, starving the estimator of spatial diversity. To systematically break this degeneracy, our architecture integrates a classical empirical observability Gramian (EMGR) planner with a learned Soft Actor-Critic (SAC) exploratory policy. A deterministic meta-supervisor actively monitors estimator reliability via Kullback-Leibler (KL) divergence, dynamically blending deterministic exploitation with learned exploration to steer the sUAS into high-information zones. Trained via a progressive curriculum and safeguarded by a strictly enforced Robust Control Barrier Function (RCBF), our RL framework achieves nearly 80% localization success on complex, mobile sources - drastically outperforming classical baselines (~30%) - while ensuring zero safety violations.
This paper studies energy-efficient operation of autonomous vehicles (AVs) in dynamic environments with moving obstacles and while communicating over mmWave channels. The obstacles induce severe attenuation of the mmWave channel resulting in a highly dynamic communication environment. In this setting, we consider the problem of jointly optimizing motion and communication energy for an AV that safely navigates among dynamic obstacles toward a designated destination while ensuring timely transmission of onboard sensing or telemetry data over mmWave channels. We then seek a real-time methodology to compute energy-efficient trajectories in a setting where dynamic obstacles induce both safety constraints and time-varying mmWave blockage, leading to tightly coupled motion-communication trade-offs. We propose a nonlinear model predictive control (NMPC) framework that enables anticipative communication and motion decision-making and energy co-optimization, augmented with a control barrier function (CBF) to ensure safety. Extensive simulation results demonstrate the effectiveness of our approach, reducing total energy consumption by up to 37.3% compared to baseline strategies. Overall, our results demonstrate that the proposed NMPC-based framework significantly enhances energy efficiency and performance of AVs under dynamic, blockage-sensitive mmWave communication constraints.
A valid control barrier function (CBF) certifies if its represented safe set can be rendered forward invariant, and the sign of its value indicates whether a state is safe or not, but it does not quantify a degree of safety beyond the binary indication. In this paper, we show that among valid CBFs representing the same safe set, interior values and gradients can be changed arbitrarily, so neither quantity determines a degree of safety that is independent of how the set is represented. We also show that whether a candidate CBF-based inequality constraint is feasible does not by itself quantify a degree of safety. In particular, infeasibility can occur either because the safe set is not controlled invariant or because the candidate CBF representation fails. This motivates our distinction between intrinsic and representational infeasibility. Finally, we introduce the invariance authority demand (IAD), a representation-independent degree of safety that quantifies the control authority required for controlled invariance and can be used to guide set or actuator repair.
Control Barrier Functions (CBFs), their High-Order variants (HOCBFs) and Exponential CBFs (ECBFs) are standard geometric tools for enforcing nonlinear safety constraints. CBFs, and their variants, offer an elegant geometric framework for nonlinear safety, yet mathematically, they reduce to continuous-time convolutions restricted by zero-memory kernels. In the presence of high-frequency measurement noise, these memoryless operators act as improper filters, leading to significant control chattering and the potential loss of active control authority due to Quadratic Program (QP) infeasibility. To address this structural limitation, this paper introduces a space-time transform that embeds dynamic temporal filtering directly into the safety constraint synthesis. By designing a proper spatio-temporal kernel, this approach inherently attenuates high-frequency noise while preserving affine control authority. Crucially, we prove the robust forward invariance of the designed STT-CBF. Monte Carlo simulations of a third-order system demonstrate that the proposed framework achieves a 100% safety rate while reducing control total variation by over 99% compared to conventional parameterized barrier methods, mitigating hardware hazards and enabling reliable deployment on physical robotic platforms.
Backup control barrier functions (bCBFs) enforce safety for input-constrained nonlinear systems using a pre-certified backup set and controller, but their performance depends strongly on this prescribed pair. This letter develops a constructive method for synthesizing a less conservative backup pair via finite horizon sum-of-squares (SOS) backward reachability. Starting from an initial backup set, we compute an SOS-certified finite horizon backward reachable set and controller that satisfy safety and input constraints while steering trajectories to the original backup set. We then provide conditions under which this certified set becomes a valid backup set for a piecewise backup controller. The resulting backup pair is integrated into the bCBF framework to certify larger safe sets.
This paper develops a certified constraint-reduction method for distributed model predictive control with tube-tightened exponential control barrier functions (eCBFs) in multi-agent systems. At each prediction stage, pairwise agent--agent and agent--obstacle eCBF conditions define halfspaces in the local control space. Rather than enforcing all such halfspaces, a geometry-adaptive subset is retained and a Farkas certificate verifies that the reduced admissible set is contained in the full tightened set. For planar inputs, cone coverage is characterized through the largest angular gap: two extreme directions suffice in the strict half-plane regime, while other geometries initialize with three retained constraints and escalate only when certification fails. Conic multipliers and nominal-aware offsets are obtained in closed form, without an auxiliary optimization, and the resulting construction preserves any nominal control already admissible for the full tightened set. Consequently, the reduced controller inherits the robust safety guarantee of the underlying tube-eCBF formulation. In a ten-follower, four-obstacle study, the method retained fewer safety constraints on average, reproduced the full filter's nominal accept/reject decisions with no true safety violations, and achieved increasing computational gains as the constraint count and prediction horizon grew.
Control invariance validates that dynamical systems have a control input that preserves a given property at all times. This paper introduces a set of sound axioms and proof rules in differential dynamic logic (dL) that enable verification of control invariance. First, the scalar and vector comparison principles, relating a system of differential equations to a comparison system such that invariance properties can be established more easily, are axiomatized in dL. This axiomatization primarily utilizes differential ghosts, which are proof-theoretic generalizations of comparison systems. Next, with the comparison principles serving as the basis, comparison invariants are introduced, and sound axioms and proof rules are derived. Comparison invariants reduce the question of control invariance to a functional inequality on its Lie derivative for a suitable class of functions, moreover, the right choice of function can result in decidable arithmetic. Furthermore, the perennially popular control barrier functions (CBFs) used in safety-critical control are shown to be a special instance of comparison invariants. This yields an axiomatization of CBFs that leads to a dedicated set of proof rules. The rules allow for the verification of CBFs, which are traditionally used for synthesizing safe controllers without verification. Lastly, comparison invariants are shown to unify several other safety verification techniques, including Darboux invariants and differential invariants, further cementing their versatility.
In this paper, we consider generalized Nash equilibrium (GNE) seeking in non-cooperative games with coupled constraint sets. Specifically, we aim to enforce safety for distributed GNE seeking, whereby the safety specifications are encoded in the coupled constraint set. To achieve this, we introduce the control barrier function (CBF) in the design of the GNE seeking dynamics. We design the dynamics for both full- and partial-information setting, where each player has knowledge of the decision information of all other players or only neighboring players, respectively. We justify the proposed dynamics by showing that the coupled constraint set is forward invariant, the equilibrium of the dynamics coincides with the exact GNE of the game, and the dynamics is asymptotically stable. Furthermore, we extend the approach to games where the agents are multi-integrators. Numerical simulations are provided to verify our results.
Safety-aware motion planning remains a challenge in robotics, especially when missions are time-critical and are under complex specifications. In this paper, we propose safety-aware-stl-mppi, a computationally efficient sampling-based receding-horizon planning framework designed to promote satisfaction of constraints expressed in Signal Temporal Logic (STL). Our approach encodes discrete-time STL formulas into candidate time-varying control barrier functions (CBF), which are integrated into a model predictive path integral (MPPI) controller. Our method inherits the benefits of low computational cost from an efficiently parallelizable sampling based planner and utilizes CBF for constraints expressed in STL. We compare against several MPPI baselines using four artificial Mars Rover planning case studies with a diverse environment and cost setups, where we show our method consistently achieving high safety and efficiency. We show a quadcopter planning experiment with NVIDIA Isaac Lab.
This paper studies the construction of control barrier functions (CBFs) for force-controlled nonholonomic mobile robots subject to relative-degree-two safety constraints arising from position-level obstacle avoidance. A scaling-based reciprocal barrier construction is proposed, in which a positive motion-dependent scaling factor is placed in the numerator of a reciprocal barrier associated with the original physical safety function. The resulting barrier is defined exactly on the interior of the physical safe set and becomes singular on its boundary, thereby preserving the certified interior domain of the original safety constraint while recovering first-order control authority. For a force-controlled nonholonomic robot model, sufficient conditions are derived under which the proposed construction defines a reciprocal CBF, and the interior of the physical safe set is forward invariant under controllers satisfying the induced reciprocal-CBF condition. A scalar strict-feedback system is further used to provide a structural interpretation of the underlying higher-relative-degree cascade under explicit structural assumptions. Numerical simulations demonstrate the induced safe-set geometry and its integration with an optimization-based control framework for obstacle avoidance.
This paper presents a safety-critical bilateral teleoperation framework for omnidirectional aerial manipulators that integrates visual and force-sensorless haptic wrench feedback. Unlike existing approaches that either rely on onboard force/torque sensors or use model-dependent wrench estimates, which may become unreliable under model uncertainties or induce unintended feedback during free-flight, our method implements a hierarchical safety filter based on control barrier functions to avoid such limitations. The safety filter, being the key contribution, explicitly accounts for tracking errors arising from physical interaction between the aerial manipulator and its surroundings while enforcing thrust limits, a factor overlooked despite its critical importance for flight safety. This safety filter adjusts the command from the operator to ensure safe and stable aerial manipulation and avoid motor saturation. The adjustment made by the filter is mapped to haptic feedback, which is intuitive to the operator and conveys information on physical interaction and impending motor saturation. By actual experiments with a hexarotor-based omnidirectional aerial manipulator, we demonstrate that the proposed method avoids haptic feedback during free-flight, provides directionally consistent feedback under physical interaction, and can be operated for diverse manipulative tasks. Moreover, an ablation study further shows that the saturation filter improves interaction stability by explicitly preventing motor saturation and informing the operator of corrective actions.
Safe and efficient shape-aware navigation in heterogeneous crowds and robot fleets remains challenging. Traditional approaches often assume homogeneous robots, sparse workspaces, simplified geometry, offline computation, or handcrafted parameters to make the problem tractable, which limits their deployment in dense crowd scenarios. Toward this end, we propose Shape-Aware Reinforcement Learned Model Predictive Control (SRL-MPC), a method for safe, efficient, and adaptive navigation in crowds with heterogeneous shapes without geometry simplification. To encode shape-aware safety, we formulate high-order control barrier function (HOCBF) constraints from geometric separation features (GSFs) based on support function transformation. A reinforcement learning (RL) framework then learns a neural policy that reads GSFs and outputs real-time MPC parameter updates, enabling the MPC solver to adapt to neighboring crowd geometries. The key advantage of SRL-MPC is that it preserves the safety structure and generalizability of MPC while integrating the adaptability and intelligence of RL. Experiments in randomized crowd scenarios with arbitrary shaped robot fleets demonstrate the effectiveness, scalability, and robustness of SRL-MPC. The results show that SRL-MPC substantially outperforms representative baselines in safety and adaptability. Project website: https://hanruihua.github.io/srl_mpc_project/
Safety filters are an effective tool for enforcing constraints in safety-critical systems, but most existing methods assume perfect state information, which is rarely available in practice. Recent work has begun to close this gap by developing filtering mechanisms that are robust to state estimation error, but these methods can still exhibit safety violations or overly conservative behavior as estimation error grows. Focusing on obstacle avoidance, we develop two new control barrier function (CBF) formulations: drift-measurement-robust (DMR)-CBFs and neural measurement-robust (NMR)-CBFs. The DMR-CBF augments the standard CBF condition with an inner optimization over the worst-case uncertainty in the drift dynamics, improving robustness to estimation error. This DMR-CBF then supervises a pretraining phase for the NMR-CBF, which replaces the inner optimization with a learned term. The NMR-CBF is subsequently finetuned through differentiable trajectory rollouts, yielding a filter that achieves empirical safety comparable to the DMR-CBF while reducing both conservativeness and computational cost. We provide theoretical analysis of the DMR-CBF along with numerical results on a planar double integrator and a 12D quadrotor, where both proposed approaches prevent collisions while other robust methods either fail or are overly conservative. Finally, we deployed the NMR-CBF on a Unitree Go2, enabling successful navigation of an obstacle field under odometry errors that caused a standard CBF to collide.
This paper presents a guide path-free multimodal trajectory planning framework for autonomous surface vehicles operating in dynamic environments. The proposed method integrates model predictive control (MPC) with a turning circle-based control barrier function (TC-CBF). Unlike conventional Euclidean distance-based CBFs (ED-CBFs), which evaluate safety solely based on proximity, the TC-CBF accounts for the nonholonomic motion and finite turning capability of a surface vehicle. Its geometric formulation identifies feasible avoidance regions according to the vehicle's turning circles and generates distinct left- and right-turning avoidance modes. These modes allow the optimization solver to explore and select topologically different trajectories without relying on globally planned guide paths, as required by many conventional multimodal planning approaches. By embedding the avoidance direction directly into the safety constraint, the proposed framework alleviates the local-minimum and deadlock problems of single-mode MPC while maintaining computational efficiency. Extensive simulations involving multiple moving vessels demonstrate that the proposed method achieves higher success rates, fewer safety violations, and smaller residual violations than single-mode baselines across all tested traffic densities.
Mission-critical intelligent systems often operate under time-varying limitations that reduce control authority and change the admissible safe operating envelope. In such settings, a safety certificate learned under nominal conditions may become invalid as system capability changes. To address this challenge, this paper proposes a degradation-aware, data-driven safety-filtering framework that learns a safe set from data, updates it online, and enforces the resulting learned barrier through a time-varying control barrier function (CBF). A nominal safe envelope is first learned from operational data using a radial basis function (RBF)-kernel support vector machine (SVM), whose decision function serves as the initial CBF candidate. To capture capability-induced safe-set contraction, a continuous-time decremental SVM update law is developed so that selected support-vector coefficients are reduced according to a degradation signal. A homotopy-smoothed SVM-CBF is then introduced to avoid discontinuous changes in the learned barrier during active-set transitions. The resulting time-varying learned barrier is enforced using a quadratic-program-based safety filter under degraded input constraints. Forward invariance of the learned time-varying safe set and recursive feasibility of the safety filter are established. Simulation results on a vertical takeoff and landing (VTOL) model show that the proposed method maintains safety under reduced control authority and avoids abrupt barrier-switching effects during safe-set contraction.
This paper presents a novel whole-body Backstepping control strategy for safe quadcopter path-following. The proposed approach introduces an integrated control scheme that combines a translational guidance controller with a rigid-body attitude controller. To guarantee asymptotic path convergence, the method utilizes a nominal Integrated Guidance and Control (IGC) based on Artificial Vector Fields (AVF). To ensure reactive safety and collision avoidance, the control law is modified using a smooth distance function within the High-Order Control Barrier Function (HOCBF) framework. The quadcopter dynamics are modeled using quaternion algebra to represent position, velocity, and attitude. By combining the Backstepping approach with HOCBF, the controller guarantees that the vehicle avoids obstacle sets while successfully converging to the target path when unobstructed. The proposed methodology is validated through software-in-the-loop simulations and real-world experimental results using the Crazyflie platform.
Allocation schemes that greedily maximize a readiness metric over the actuator fiber bundle of an overactuated multirotor produce commands that jump between disconnected optimal strata, demanding actuator rates no motor can deliver; effort-minimizing schemes are continuous but cannot guarantee that wrench-rate authority stays above any certified level. We reconcile the two by treating authority as a forward-invariant quantity: a control barrier function on the log-determinant of the drag-aware actuator-authority co-metric, enforced at torque level by a quadratic program in the allocation null space. A single design inequality renders the certified set compact and strictly interior to the actuator box, with the readiness cost of any rotor deactivation given in closed form as $\ln(n/(n{-}m))$ for symmetric designs. Tracking is sacrificed only through an explicit alignment ratio, with wrench error bounded by $\mathcal{O}(ρ^{-1/2})$ and a robust variant handles motor-parameter uncertainty with a closed-form floor shift independent of the airframe matrix. On a hexarotor and a fully-actuated octorotor the closed-form gap matches simulation to machine precision; in the authority-scarce regime greedy maximization violates the certified floor and commits wrench errors up to eighty times larger than the proposed filter, which holds invariance of the certified set at negligible tracking cost.
This paper presents a control framework for formation tracking and rigidity maintenance in heterogeneous multi-robot systems with nonlinear dynamics under sensing range constraints. Since formation tracking alone does not ensure rigidity maintenance with a limited sensing range, despite rigidity being a prerequisite for establishing and preserving a unique formation, our work integrates both objectives through a single Control Barrier Function (CBF)-like constraint within a quadratic optimization framework. The proposed distributed controller requires only local relative information from neighbors, as verified with simulation case studies.
Designing effective trading strategies using reinforcement learning remains challenging due to delayed and noisy rewards, poor exploration, and the difficulty of enforcing explicit risk constraints. In this work, we propose BRaG, a barycenter-based adversarial inverse reinforcement learning framework for stock trading that learns trading behavior from multiple heterogeneous expert strategies. BRaG aggregates expert demonstrations using a performance-weighted Wasserstein barycenter, yielding a stable pseudo-expert representation that captures shared structure across diverse trading styles. This representation is used to pretrain a trading policy via adversarial imitation learning, which alleviates unstable exploration during reinforcement learning. The pretrained policy is subsequently refined using reinforcement learning with true market rewards. To ensure risk-aware decision-making, BRaG incorporates control barrier functions that constrain action execution and regularize policy learning to satisfy drawdown limits. We evaluate the proposed approach on four major global equity markets, including the US, UK, Indian, and Taiwanese indices. Across all the markets, the proposed approach achieves stronger performance than both classical trading rules and recent deep reinforcement learning methods, while exhibiting more stable risk characteristics.
Control barrier functions (CBFs) provide a systematic framework for enforcing safety constraints in nonlinear control systems. However, their implementation typically relies on accurate system models, which can limit their applicability in the presence of significant modeling uncertainties or unknown dynamics. This paper proposes a model-free framework for the computation of recursive control barrier functions based on the ultra-local model approach that leverages online estimation of the unknown system dynamics to construct CBF constraints. This approach does not require an explicit model of the system dynamics and enhances robustness with respect to disturbances and model mismatch. The resulting control architecture enables the enforcement as well as the anticipation of safety constraints for systems with higher relative degree. The effectiveness of the proposed approach is illustrated on the adaptive cruise control benchmark.
Operating teams of autonomous aircraft in dynamic, uncertain, and potentially adversarial environments requires safety protocols that are reliable yet selective, and allow agents to fly in close proximity while making progress toward mission objectives. We introduce adversarial time-to-collision (aTTC), a risk metric that quantifies, for a given agent, how quickly any surrounding agent could reach it assuming adversarial intent. We embed aTTC into the control barrier function (CBF) framework, defining the barrier directly in time rather than distance or velocity. The resulting aTTC-CBF is inherently anticipatory: agents modulate their own velocity based not on whether a peer is on a collision course, but on how quickly one could reach collision given its dynamical constraints. A differentiable neural-network surrogate makes the aTTC computable in real time within a standard CBF quadratic program. Across long time-horizon simulations of 3D independent-pursuit and formation-flight scenarios, the aTTC-CBF achieves up to twice the waypoint progress at half the collision rate of a higher-order distance-based CBF baseline.
This paper presents a control barrier function-based method for real-time in-domain congestion control of the Lighthill-Whitham-Richards traffic model. Traffic congestion is formulated as a distributed safety control problem, leading to a infinite-dimensional optimization problem. Through the discretization and Karush-Kuhn-Tucker (KKT) analysis, the problem is converted into a high-dimensional quadratic program. A structure-exploiting primal-dual active set algorithm is then developed to compute the safe control input in real time, with convergence guarantees. Numerical simulations with different nominal controllers demonstrate the effectiveness and real-time feasibility of the proposed approach.
This paper studies safety analysis and controller synthesis for partially observable nonlinear control systems. We extend the control barrier--value function (CBVF) framework, which combines Hamilton--Jacobi reachability and control barrier functions, to settings where full state information is not available and control is based on an estimated state. Given an estimator, we apply conformal prediction to the estimation error and obtain an error bound at a user-chosen miscoverage level. We incorporate this bound into the estimator-space safety analysis and define a CBVF-based safety certificate for partially observable systems. We then derive a finite-horizon probabilistic safety guarantee for the true system state. Finally, we propose a QP-based online safety filter for systems affine in the control and disturbance, whose solution enforces the CBVF safety condition in real time against bounded disturbance. The proposed framework is illustrated on a partially observable obstacle-avoidance case study.
Fast charging of Lithium-ion batteries can lead to a significant temperature rise, which can cause serious risks to battery safety and lifetime. To ensure safe battery operation, thermal constraints must be enforced during the fast charging process. However, the core temperature of the battery cannot be directly measured in practice, which makes real-time safety enforcement challenging. This paper proposes a framework that incorporates core temperature estimates from Kolmogorov-Arnold Network within robust control barrier function (KAN-rCBF) constraints for battery fast-charging. The algorithm utilizes measurements from battery surface temperature, coolant temperature, coolant power, and charging current to solve a quadratic programming problem under safety constraints. We prescribe analytical safety guarantees for this optimal charging policy under KAN estimation errors and model uncertainty. Simulation results show that the proposed method maintains a safe battery temperature while achieving charging times comparable to the state-of-the-art method, where the latter fails to guarantee the same level of thermal safety.
We present a robust safety-filtering framework for input-constrained underactuated linear systems subject to unknown disturbances. A baseline H-$\infty$ input is derived from a zero-sum differential game, while a disturbance observer supplies an estimate and a transient error bound. The baseline input is adjusted using the disturbance estimate, while the estimate and its error bound are used to define robust high-order control barrier function constraints; forward invariance holds as long as the admissible-input set remains nonempty. For scalar-input systems, pointwise feasibility is determined from an exact input interval, and the interval width defines the feasibility margin. A finite-horizon H-$\infty$ performance balance accounts for the accumulated deviation of the applied input from the baseline H-$\infty$ policy. Simulations on a linearized two-wheeled balancing robot show how position and body-pitch constraints compete for the same bounded wheel-torque input.
Differentiable predictive control (DPC), a self-supervised learning approach for approximating explicit model predictive control (MPC) policies, offers significant computational advantages over online optimization-based MPC. However, feasibility guarantees, a core requirement for safe control, are currently provided either probabilistically or via online safety filters. The lack of rigorous feasibility guarantees for offline policy optimization remains an open problem. This paper establishes deterministic feasibility guarantees for DPC using a novel topological analysis of the induced reachable safe set, without requiring online safety filters. By exploiting the inherent model-based nature of DPC, in which differentiable system dynamics are embedded directly into the computational graph, we analyze the properties of the learned control policies and the corresponding system states from topological and geometric perspectives. Inspired by our theoretical analysis, we propose a novel self-supervised offline policy learning strategy that utilizes a proxy loss with Control Barrier Functions (CBFs). Crucially, these properties not only significantly improve policy training but also enable the derivation of strict, deterministic feasibility guarantees from a finite number of training samples. Extensive closed-loop simulations validate our theoretical findings, demonstrating that the empirical constraint violations monotonically decrease to zero as the training sample size increases. Ultimately, this work illustrates that DPC policy optimization yields formal safety certificates that are structurally unattainable with conventional black-box methods, e.g., reinforcement learning (RL) or supervised learning-based approximate MPC, thereby providing a new perspective on feasibility guarantees in learning-based control.
Reduced-order models based on Cosserat-rod theory are now well established, and modeling theory is no longer the primary bottleneck in soft-robot control. Their implementations, however, do not support the differentiable, GPU-parallel, and control-oriented workflows that underpin advanced rigid-robotics applications. Here, we fill this gap with SoRoMoX (Soft Robot Models in JAX), a fully numerical, JIT-compilable Python/JAX framework. SoRoMoX implements articulated, Piecewise Constant Strain, and Variable Strain models through a unified, control-ready interface that provides inertia matrices, gravitational and elastic forces, Jacobians, and their derivatives. To our knowledge, it is the first rod/strain-based soft-robot modeling framework that runs directly on GPUs and is end-to-end differentiable with respect to states, inputs, and parameters. Sequential CPU rollouts are up to 18.1x faster than state-of-the-art alternatives, while GPU-parallel rollouts increase throughput by up to 234.6x. This performance enables workflows that were previously impractical or impossible: static-equilibrium system identification with 66% lower marker RMSE; residual-force learning with a further 64% reduction; computed-torque tracking with RMSE reduced by a factor of approximately 500 relative to model-free PD; control-gain optimization with up to 62% lower loss than untuned gains; safety-constrained control using high-order control barrier functions to keep the peak contact force within a prescribed 5 N bound, compared with 33.5 N without the safety constraint; and reinforcement-learning policy training up to 7x faster than a CPU PyElastica discrete-rod baseline through massively parallel rollouts.
Safe actor-critic control often treats barrier filtering, uncertainty estimation, and experience replay as separate modules, even though each changes the data used for learning and control. We develop an integrated architecture in which the uncertainty estimate updates the obstacle geometry used by a control barrier function, filter interventions and estimation residuals determine replay priority, and the critic learns from the executed rather than nominal action. We instantiate the architecture on a two-dimensional robot-navigation task with corrupted obstacle measurements and compare six component-matched configurations under common training budgets, random seeds, sensor streams, exploration, and disturbances. Evaluation includes a moderate post-training test, an eleven-level perception-noise sweep, and an exploratory extreme-stress test at multiplier $6.0$. In the extreme test, the integrated configuration recorded no contacts and reached the goal in all five evaluation seeds. Its mean cost was $7.63\pm0.44$ and its obstacle-belief root-mean-square error was $3.52\pm0.55$ cm. The uncertainty-estimation ablation also recorded no contacts but reached the goal in four of five seeds, with mean cost $8.96\pm2.08$ and belief error $11.08\pm1.23$ cm. A finite-training bound clarifies replay exposure, and a robust barrier condition states the required estimation-error and feasibility assumptions. The results support coupling estimation, safety filtering, and replay on this benchmark; broader safety and convergence claims require further study.
Safely navigating polytopic environments while respecting the dynamics, control, and exact geometry of the underlying system is a challenge in robotics. Control barrier functions (CBFs) synthesize safe control policies by rendering the safe set forward invariant, but many existing CBF-based methods approximate polytopes using conservative smooth shapes, such as spheres or ellipsoids, to obtain explicit differentiable distance functions. In this article, we propose an exact Signed Distance Function (SDF) formulation for a {\it polytopic} robot and {\it polytopic} obstacles and integrate it with nonsmooth CBFs. Leveraging Minkowski operations, the proposed method computes the exact SDF via companion convex programs in both the collision-free (positive-sign) and in-collision (negative-sign) cases. Furthermore, by exploiting the convenient geometric properties of 2D Minkowski operations and the optimality conditions of the two companion convex programs, we derive a unified analytical expression for the gradient of the exact SDF via sensitivity analysis. The exact rotational gradient further reveals a previously masked class of local minima induced by the coupling between geometry and nonholonomic kinematics. We demonstrate the effectiveness of the proposed framework through a pure-translation case and three scenarios with unicycle models involving recovery from an unsafe initialization and single- and multiple-obstacle avoidance. Comparisons with baseline methods highlight how the proposed framework enables non-conservative maneuvers and safety recovery.
In vision-aided navigation and visual-inertial odometry, the quality of triangulated three-dimensional feature positions is a fundamental prerequisite for state estimation accuracy. Triangulation becomes ill-conditioned or even impossible when a camera undergoes pure rotation without translation, or when the observed bearing vectors provide insufficient parallax. Even though visual-inertial odometry has been extensively studied, the active maintenance of feature-observability during navigation has not been sufficiently addressed in the literature. To address this gap, this study presents TANGO-VIO, a triangulation-aware navigation framework that embeds a log-determinant metric of the feature-wise stacked-bearing matrix into a control barrier function. In this proposed method, the observability guarantee is established in the feature-geometric sense by enforcing a lower bound on the aggregate triangulation-information metric through a nominal-direction-weighted minimum-deviation velocity correction. The proposed architecture is evaluated through software-inthe- loop simulations and real flight experiments. The results show improved triangulation conditioning under low-parallax motion, while the flight response closely reproduces the corresponding simulation behavior and confirms the practical realizability of the proposed safety filter. Supplementary materials are available on the project webpage.
This article presents a modular inference framework that integrates Flow Matching generative models with formal Control Barrier Function (CBF) safety guarantees. Unlike existing methods that apply external safety filters to a model's final output, our approach modifies the Flow Matching denoising process within the model to inherently generate safe trajectories. By employing a smooth Log-Sum-Exponential aggregate barrier, we enforce safety over entire action chunks. This aggregate barrier ensures a minimal increase in computational overhead and does not alter the semantic intent of the model. We show that, within the proposed framework, the 2-Wasserstein distance between the generated distribution and the target distribution remains bounded. Our method eliminates the need for safety-specific datasets or costly model retraining, providing a versatile solution for safe inference. We validate the approach on two robotic manipulation platforms and a 2D navigation benchmark, verifying that our framework achieves reliable safety without degrading the success rate of the model.
Ensuring operation of aerospace systems within prescribed flight envelope limits is a fundamental requirement for modern flight control architectures. Flight envelope protection aims to prevent violations of aerodynamic and structural constraints, thereby mitigating risks such as stall and excessive load factors. Control barrier functions (CBFs) have emerged as a principled tool for enforcing safety by ensuring that the system state remains within a prescribed safe set. In most existing approaches, safety constraints are imposed at the control input-level based on an open-loop model of the system. While this open-loop model-based CBF formulation enables modular design, it may alter the closed-loop system dynamics, potentially compromising robustness guarantees and complicating integration into existing flight control architectures. This paper proposes a closed-loop model-based control barrier function (CLM-CBF) framework for flight envelope protection. The key idea is to enforce safety at the reference-level using an explicit model of the closed-loop system, thereby preserving the stability and robustness properties of the underlying controller. This formulation enables safety filtering without modifying the control law, facilitating modular integration and retrofitting into existing systems.
In this paper, a computationally lightweight approximate robust nonlinear model predictive control (NMPC) law is proposed based on a pair of input-to-state control Lyapunov function and robust control barrier function. The result builds upon and augments a recently introduced nominal infinitesimal- horizon NMPC scheme which permits small-sized quadratic programs to compute the feedback law for nonlinear constraint systems on embedded hardware in real time. Numerical experiments for nonlinear constrained spacecraft control and comparison to other robust NMPC schemes from the literature demonstrate the effectiveness of the proposed scheme.
This paper presents an adaptive safety-critical control framework for flight envelope protection (FEP) of hypersonic glide vehicles (HGVs) under model uncertainty. The proposed architecture treats input and state constraints through two complementary but distinct mechanisms. At the input end, an adaptive controller with a calibrated closed-loop reference model (CCRM) is designed to accommodate magnitude-limited control inputs and the effects of actuator saturation. Building on this input-constrained adaptive control architecture, flight envelope state constraints are enforced at the state end by an error-based safety filter (EBSF) based on control barrier functions (CBFs). The EBSF modifies the reference command and adapts the admissible safe set online using the measured mismatch between the reference model and the uncertain plant, thereby preserving forward invariance during transient adaptation. Simulation results for the DLR generic hypersonic glide vehicle 2 (GHGV-2) demonstrate stable, high-performance tracking under magnitude-limited control inputs while maintaining flight envelope constraints in the presence of model uncertainty.
Control barrier functions (CBFs) have become an important controller design tool for autonomous systems subject to safety constraints. Despite their popularity, recent works have shown that CBF-based controllers can destabilize the internal dynamics of the system. In this paper, we consider linear systems with affine safety constraints and design linear feedback controllers that satisfy high-order CBF (HOCBF) constraints while rendering the origin globally exponentially stable. We first characterize the exact class of all linear gain matrices that globally satisfy the HOCBF constraints, including necessary and sufficient conditions for when this class is nonempty. Then, by leveraging the recently introduced notion of CBF output dynamics and CBF internal dynamics, we provide the necessary and sufficient conditions for the existence of stabilizing gain matrices within that class. Finally, we show that Linear Quadratic Regulator (LQR) and robust control problems can be solved while being constrained within this class of safe and stabilizing gain matrices, through standard linear control techniques such as algebraic Riccati equations (AREs) and Linear Matrix Inequalities (LMIs). We illustrate our results in a simulation example.
We propose a notion of robust adaptive backup control barrier functions for nonlinear control affine systems with parametric uncertainty in both the drift dynamics and actuation matrix. Backup control barrier functions guarantee safety by predicting the system's trajectory under a pre-certified safe controller. However, these predictions rely on the model and can be inaccurate when the system contains unknown parameters. To address this issue, we estimate the unknown parameters using element-wise certified adaptive estimators that provide a parameter adaptation law and component-wise estimation error bounds. We compute the backup flow using the estimated model and tighten the safety conditions using these certified bounds. The resulting safety conditions account for the sensitivity of the predicted flow to parameter estimation errors. Moreover, to handle uncertainty in the actuation matrix, we use a duality-based reformulation that enables the use of a computationally efficient quadratic-program-based safety filter. We prove that controllers satisfying the proposed robust adaptive backup control barrier function constraints guarantee safety under parametric uncertainty and input constraints.
We consider the problem of learning high-dimensional semi-global feedback controllers under hard safety constraints enforced by control barrier functions (CBFs). Incorporating CBFs into end-to-end policy training requires embedding a quadratic-program-based safety filter as an optimization layer, but computational and differentiation bottlenecks have largely restricted prior approaches to low-dimensional systems, typically with at most 16 state dimensions. We address this limitation by combining operator splitting with the recently developed Jacobian-Free Backpropagation (JFB) method to enable scalable end-to-end training while preserving hard safety guarantees through the CBF safety filter. We justify this training methodology theoretically using nonsmooth analysis techniques and demonstrate its effectiveness on high-dimensional multi-agent nonlinear control problems with state and control dimensions up to 1200 and 400, respectively.
Multi-drone payload transportation has emerged as a promising research paradigm with potential applications in construction, logistics, and disaster response. However, the complex coupled dynamics among drones, cables, and payloads pose significant challenges, and existing approaches remain limited in safety and scalability, particularly in dynamic and unstructured environments. In this work, we propose a learning-based framework for safe and scalable multi-drone cooperative payload transport. We introduce a minimal 2D abstraction that preserves the task-relevant drone-payload coupling required for coordination and safety, while remaining computationally efficient for large-scale learning. Using domain randomization over team size and physical parameters, we train a fully distributed policy via Discrete Graph Control Barrier Function Proximal Policy Optimization (DGPPO), enabling robust zero-shot sim-to-real transfer without fine-tuning. Extensive real-world evaluations demonstrate that a single learned policy generalizes across varying team sizes and task scenarios. Furthermore, multi-group hardware experiments show that the same policy can safely operate in dynamic environments, where other drone teams act as moving obstacles. These results indicate that the proposed framework enables efficient, safe, and scalable multi-drone payload transportation with strong generalization to complex real-world conditions.
Aquatic self-reconfigurable robots must assemble into desired shapes while ensuring safe interactions among multiple agents. This paper proposes a hybrid framework that combines distributed Model Predictive Control (MPC) with Control Barrier Functions (CBFs) for multi-agent shape formation and reconfiguration. Given a desired shape and target assignment, a distributed MPC scheme, solved via the Alternating Direction Method of Multipliers (ADMM), computes coordinated trajectories through local optimization and information exchange. To ensure safety in real time, distributed CBF-based filters are applied to enforce inter-agent collision avoidance. The proposed approach leverages the predictive capabilities of MPC to mitigate local minima, while CBFs provide formal safety guarantees despite the nonconvexity of the underlying optimization problem. Simulation results with up to 25 agents and experimental validation with four physical robots demonstrate the effectiveness and scalability of the framework.
Haptic feedback provides an implicit channel for communicating safety intentions during human-robot shared control. Existing haptic guidance systems typically employ predefined intervention strategies that cannot accommodate the diverse safety preferences of individual users or application scenarios. To address this limitation, we propose a Learning from Haptics (LfH) framework that learns user-preferred safety interventions from sparse demonstrations, eliminating the need for manual trial-and-error design. Our framework is built on a differentiable Control Barrier Function (CBF)-based optimization layer that automatically adjusts the underlying safety parameters to match the demonstrated haptic responses. Instead of tuning controller parameters directly, users teach the system how they expect it to intervene during teleoperation. The resulting haptic guidance reflects the demonstrated intervention preferences while preserving the intuitive interaction of haptic shared control. Simulation and hardware experiments demonstrate that the proposed framework can learn personalized safety interventions from sparse user input and reduce the mismatch between the generated haptic feedback and the demonstrated preferences.
Long-reach drilling booms must reach successive poses without self-collision. Moving from operator-supervised control toward autonomy requires collision-aware motion planning and execution. For the Sandvik SB60, this study adapts established methods by integrating pose-parameterized planning with a capsule-based control barrier function quadratic program (CBF-QP) in measured-state inverse kinematics (IK). A fixed task-specific parameter set within each task generates waypoints, detours, timed references, and chained motion without target-specific retuning. The offline detour planner screens candidate waypoints using 23 selected rod-segment-to-body-region distances, whereas the online CBF-QP filters joint velocities using 14 configured capsule-pair constraints from a nine-primitive whole-body capsule model. Evaluation considers two drilling tasks in a manufacturer-developed SB60 Simscape Multibody model: a five-target restricted-orientation tour and a three-target full-pose tour. Across several hundred thousand samples, the method produced zero IK failures, generated several detour waypoints, achieved millimetre-level mean final-position error, and recorded no sampled CBF margins below the reported thresholds.
This paper investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next, we implement vector Lyapunov function approach to propose a novel high-order control Lyapunov function (HOCLF) for the stabilization control problem. The relations between the proposed and existing HOCBFs are discussed. Afterwards, the compatibility of the proposed HOCLF and HOCBF is addressed to guarantee the stabilization and safety control objectives simultaneously, and thus the optimal controller is established. Finally, a numerical example from the navigation problem of quadrotors is presented to illustrate the efficacy of the derived results.
This paper presents a safety-critical distributed nonlinear model predictive control (DNMPC) framework for cooperative payload transportation by teams of quadrupedal robots. The proposed approach models the robotic team and the shared payload as a dynamically coupled networked system with rigid holonomic coupling constraints arising from cooperative transportation. To enable distributed real-time optimization, the centralized finite-horizon optimal control problem is decomposed into parallel local NMPC subproblems coordinated through the alternating direction method of multipliers (ADMM). The resulting distributed framework enforces consensus over both payload-state and interaction-wrench trajectories while explicitly incorporating acceleration-level holonomic coupling constraints within the distributed predictive control formulation. Safety-critical obstacle avoidance constraints for both the robotic agents and payload are enforced using higher-order control barrier functions (HOCBFs). The framework is validated through numerical simulations with teams of two, three, and four quadrupedal robots transporting shared payloads in cluttered environments. Real-time experiments on two- and three-robot teams demonstrate safe and robust transportation under payload uncertainty and external disturbances. Compared with centralized NMPC, the proposed framework achieves up to 23% reduction in average NLP solve time while maintaining comparable closed-loop performance. Ablation studies further demonstrate robustness to communication delays and show that explicit payload-state consensus and holonomic constraints substantially improve payload tracking and distributed coordination over existing wrench-only consensus formulations.
Autonomous rendezvous and proximity operations (RPO) in adversarial orbital environments require guidance architectures balancing target pursuit, safety preservation, and real-time adaptability under dynamically evolving interaction conditions. Although learning-based approaches show promise, their application to safety-critical orbital robotics remains limited by concerns regarding interpretability, robustness, and constraint awareness. This work presents an adaptive Model Predictive Control (MPC) framework for autonomous spacecraft RPO in multi-agent adversarial scenarios. The proposed architecture combines a constrained receding-horizon MPC formulation with a data-driven supervisory tuning layer that adjusts controller parameters from offline closed-loop evaluation and online interaction geometry. Relative motion follows Clohessy-Wiltshire (CW) dynamics, enabling computationally efficient finite-horizon prediction and real-time quadratic optimization. The MPC formulation incorporates actuator limits, predictive keep-out-zone constraints, slack-variable feasibility handling, and optional Control Barrier Function (CBF) safety filtering. Rather than generating thrust commands directly, the adaptive layer modifies interpretable MPC parameters, including tracking weights, safety penalties, minimum-separation objectives, and keep-out-zone objectives. The framework was evaluated in the official Kerbal Space Program Differential Game (KSPDG) Capture-the-Satellite environment through Monte Carlo simulations. Results demonstrate improved closed-loop robustness, adaptive maneuvering behavior, and rendezvous performance compared with fixed-parameter MPC while preserving safety-aware operation and real-time feasibility, providing a modular, interpretable foundation for adaptive spacecraft RPO.
Safe model-based reinforcement learning (RL) often bridges control-theoretic analysis and RL for robots to safely explore (partially) unknown system dynamics while deriving control actions for task efficiency. The control performance and safety assurance typically rely on prior knowledge of partially modeled nominal system dynamics and the data-driven models that compensate for residual model uncertainties. However, existing methods often overlook the structure of residual model uncertainties (e.g., components affine in control), which could lead to overly conservative robot behaviors or invalid safety guarantees under the safe learning-based controllers. This paper proposes a safe reinforcement learning framework that learns control-affine dynamics with a certifiable data-driven safe policy using control barrier functions (CBF). Specifically, we first use Control-Affine Random Fourier Features (ARFF) to model robot dynamics in a control-affine form, which offers computational efficiency that scales with dataset size and reduces potential model bias for model-based reinforcement learning. Then, a model-free, efficient uncertainty quantification method using adaptive conformal prediction (ACP) is applied to quantify the uncertainty in the safety constraint arising from the learned control-affine dynamics. This allows for data-driven safety assurance amenable to principled and efficient controller synthesis with CBF. Simulation results on the cartpole and the 3D quadrotor platforms demonstrate the effectiveness of the proposed framework.
Control barrier functions (CBFs) provide formal safety guarantees for constrained nonlinear systems, but their effectiveness relies on accurate system dynamics. In high-dimensional manipulators subject to unknown disturbances and model uncertainties, fixed safety constraints constructed from nominal dynamics may become inconsistent with the actual system behavior, leading to safety degradation or excessive conservatism. This paper proposes a dynamic constraint reconstruction based control barrier function (DCR-CBF) framework for safety-critical control of disturbed robotic manipulators. An extended state observer is employed to estimate lumped disturbances online, and the estimated disturbance is incorporated into high-order control barrier functions to reconstruct safety constraints according to the estimated true dynamics. To address estimation inaccuracies, a safety margin is introduced, and a sufficient condition is derived to guarantee forward invariance under bounded estimation errors. Simulation studies on a 4-DOF excavation manipulator demonstrate that the proposed DCR-CBF method achieves zero safety violation under strong unknown disturbances while significantly improving trajectory-tracking performance compared with standard and robust CBF methods.
Robots navigating under occlusion may enter states from which no admissible input can avoid a dynamic obstacle once it becomes visible. We present OcclusionCBF, a safety filter that extends backup control barrier functions to reachable-occupancy predictions for potentially hidden dynamic obstacles in occluded regions. The method certifies a prescribed backup rollout against collision-inflated occupancy and a verified terminal set, yielding affine constraints for minimally invasive quadratic-program filtering. We establish recursive feasibility of the resulting safety filter, and collision avoidance for every hidden-obstacle motion covered by the occupancy prediction. Randomized benchmarks, MetaUrban simulations, and hardware experiments demonstrate improved task success over reactive and occlusion-aware predictive baselines with millisecond-scale computation.
A valid control barrier function (CBF) certifies if its represented safe set can be rendered forward invariant, and the sign of its value indicates whether a state is safe or not, but it does not quantify a degree of safety beyond the binary indication. In this paper, we show that among valid CBFs representing the same safe set, interior values and gradients can be changed arbitrarily, so neither quantity determines a degree of safety that is independent of how the set is represented. We also show that whether a candidate CBF-based inequality constraint is feasible does not by itself quantify a degree of safety. In particular, infeasibility can occur either because the safe set is not controlled invariant or because the candidate CBF representation fails. This motivates our distinction between intrinsic and representational infeasibility. Finally, we introduce the invariance authority demand (IAD), a representation-independent degree of safety that quantifies the control authority required for controlled invariance and can be used to guide set or actuator repair.
Control Barrier Functions (CBFs), their High-Order variants (HOCBFs) and Exponential CBFs (ECBFs) are standard geometric tools for enforcing nonlinear safety constraints. CBFs, and their variants, offer an elegant geometric framework for nonlinear safety, yet mathematically, they reduce to continuous-time convolutions restricted by zero-memory kernels. In the presence of high-frequency measurement noise, these memoryless operators act as improper filters, leading to significant control chattering and the potential loss of active control authority due to Quadratic Program (QP) infeasibility. To address this structural limitation, this paper introduces a space-time transform that embeds dynamic temporal filtering directly into the safety constraint synthesis. By designing a proper spatio-temporal kernel, this approach inherently attenuates high-frequency noise while preserving affine control authority. Crucially, we prove the robust forward invariance of the designed STT-CBF. Monte Carlo simulations of a third-order system demonstrate that the proposed framework achieves a 100% safety rate while reducing control total variation by over 99% compared to conventional parameterized barrier methods, mitigating hardware hazards and enabling reliable deployment on physical robotic platforms.
Backup control barrier functions (bCBFs) enforce safety for input-constrained nonlinear systems using a pre-certified backup set and controller, but their performance depends strongly on this prescribed pair. This letter develops a constructive method for synthesizing a less conservative backup pair via finite horizon sum-of-squares (SOS) backward reachability. Starting from an initial backup set, we compute an SOS-certified finite horizon backward reachable set and controller that satisfy safety and input constraints while steering trajectories to the original backup set. We then provide conditions under which this certified set becomes a valid backup set for a piecewise backup controller. The resulting backup pair is integrated into the bCBF framework to certify larger safe sets.
This paper develops a certified constraint-reduction method for distributed model predictive control with tube-tightened exponential control barrier functions (eCBFs) in multi-agent systems. At each prediction stage, pairwise agent--agent and agent--obstacle eCBF conditions define halfspaces in the local control space. Rather than enforcing all such halfspaces, a geometry-adaptive subset is retained and a Farkas certificate verifies that the reduced admissible set is contained in the full tightened set. For planar inputs, cone coverage is characterized through the largest angular gap: two extreme directions suffice in the strict half-plane regime, while other geometries initialize with three retained constraints and escalate only when certification fails. Conic multipliers and nominal-aware offsets are obtained in closed form, without an auxiliary optimization, and the resulting construction preserves any nominal control already admissible for the full tightened set. Consequently, the reduced controller inherits the robust safety guarantee of the underlying tube-eCBF formulation. In a ten-follower, four-obstacle study, the method retained fewer safety constraints on average, reproduced the full filter's nominal accept/reject decisions with no true safety violations, and achieved increasing computational gains as the constraint count and prediction horizon grew.
Control invariance validates that dynamical systems have a control input that preserves a given property at all times. This paper introduces a set of sound axioms and proof rules in differential dynamic logic (dL) that enable verification of control invariance. First, the scalar and vector comparison principles, relating a system of differential equations to a comparison system such that invariance properties can be established more easily, are axiomatized in dL. This axiomatization primarily utilizes differential ghosts, which are proof-theoretic generalizations of comparison systems. Next, with the comparison principles serving as the basis, comparison invariants are introduced, and sound axioms and proof rules are derived. Comparison invariants reduce the question of control invariance to a functional inequality on its Lie derivative for a suitable class of functions, moreover, the right choice of function can result in decidable arithmetic. Furthermore, the perennially popular control barrier functions (CBFs) used in safety-critical control are shown to be a special instance of comparison invariants. This yields an axiomatization of CBFs that leads to a dedicated set of proof rules. The rules allow for the verification of CBFs, which are traditionally used for synthesizing safe controllers without verification. Lastly, comparison invariants are shown to unify several other safety verification techniques, including Darboux invariants and differential invariants, further cementing their versatility.
Safety-aware motion planning remains a challenge in robotics, especially when missions are time-critical and are under complex specifications. In this paper, we propose safety-aware-stl-mppi, a computationally efficient sampling-based receding-horizon planning framework designed to promote satisfaction of constraints expressed in Signal Temporal Logic (STL). Our approach encodes discrete-time STL formulas into candidate time-varying control barrier functions (CBF), which are integrated into a model predictive path integral (MPPI) controller. Our method inherits the benefits of low computational cost from an efficiently parallelizable sampling based planner and utilizes CBF for constraints expressed in STL. We compare against several MPPI baselines using four artificial Mars Rover planning case studies with a diverse environment and cost setups, where we show our method consistently achieving high safety and efficiency. We show a quadcopter planning experiment with NVIDIA Isaac Lab.
This paper studies the construction of control barrier functions (CBFs) for force-controlled nonholonomic mobile robots subject to relative-degree-two safety constraints arising from position-level obstacle avoidance. A scaling-based reciprocal barrier construction is proposed, in which a positive motion-dependent scaling factor is placed in the numerator of a reciprocal barrier associated with the original physical safety function. The resulting barrier is defined exactly on the interior of the physical safe set and becomes singular on its boundary, thereby preserving the certified interior domain of the original safety constraint while recovering first-order control authority. For a force-controlled nonholonomic robot model, sufficient conditions are derived under which the proposed construction defines a reciprocal CBF, and the interior of the physical safe set is forward invariant under controllers satisfying the induced reciprocal-CBF condition. A scalar strict-feedback system is further used to provide a structural interpretation of the underlying higher-relative-degree cascade under explicit structural assumptions. Numerical simulations demonstrate the induced safe-set geometry and its integration with an optimization-based control framework for obstacle avoidance.
Safety filters are an effective tool for enforcing constraints in safety-critical systems, but most existing methods assume perfect state information, which is rarely available in practice. Recent work has begun to close this gap by developing filtering mechanisms that are robust to state estimation error, but these methods can still exhibit safety violations or overly conservative behavior as estimation error grows. Focusing on obstacle avoidance, we develop two new control barrier function (CBF) formulations: drift-measurement-robust (DMR)-CBFs and neural measurement-robust (NMR)-CBFs. The DMR-CBF augments the standard CBF condition with an inner optimization over the worst-case uncertainty in the drift dynamics, improving robustness to estimation error. This DMR-CBF then supervises a pretraining phase for the NMR-CBF, which replaces the inner optimization with a learned term. The NMR-CBF is subsequently finetuned through differentiable trajectory rollouts, yielding a filter that achieves empirical safety comparable to the DMR-CBF while reducing both conservativeness and computational cost. We provide theoretical analysis of the DMR-CBF along with numerical results on a planar double integrator and a 12D quadrotor, where both proposed approaches prevent collisions while other robust methods either fail or are overly conservative. Finally, we deployed the NMR-CBF on a Unitree Go2, enabling successful navigation of an obstacle field under odometry errors that caused a standard CBF to collide.
This paper presents a novel whole-body Backstepping control strategy for safe quadcopter path-following. The proposed approach introduces an integrated control scheme that combines a translational guidance controller with a rigid-body attitude controller. To guarantee asymptotic path convergence, the method utilizes a nominal Integrated Guidance and Control (IGC) based on Artificial Vector Fields (AVF). To ensure reactive safety and collision avoidance, the control law is modified using a smooth distance function within the High-Order Control Barrier Function (HOCBF) framework. The quadcopter dynamics are modeled using quaternion algebra to represent position, velocity, and attitude. By combining the Backstepping approach with HOCBF, the controller guarantees that the vehicle avoids obstacle sets while successfully converging to the target path when unobstructed. The proposed methodology is validated through software-in-the-loop simulations and real-world experimental results using the Crazyflie platform.
Allocation schemes that greedily maximize a readiness metric over the actuator fiber bundle of an overactuated multirotor produce commands that jump between disconnected optimal strata, demanding actuator rates no motor can deliver; effort-minimizing schemes are continuous but cannot guarantee that wrench-rate authority stays above any certified level. We reconcile the two by treating authority as a forward-invariant quantity: a control barrier function on the log-determinant of the drag-aware actuator-authority co-metric, enforced at torque level by a quadratic program in the allocation null space. A single design inequality renders the certified set compact and strictly interior to the actuator box, with the readiness cost of any rotor deactivation given in closed form as $\ln(n/(n{-}m))$ for symmetric designs. Tracking is sacrificed only through an explicit alignment ratio, with wrench error bounded by $\mathcal{O}(ρ^{-1/2})$ and a robust variant handles motor-parameter uncertainty with a closed-form floor shift independent of the airframe matrix. On a hexarotor and a fully-actuated octorotor the closed-form gap matches simulation to machine precision; in the authority-scarce regime greedy maximization violates the certified floor and commits wrench errors up to eighty times larger than the proposed filter, which holds invariance of the certified set at negligible tracking cost.
This paper presents a control framework for formation tracking and rigidity maintenance in heterogeneous multi-robot systems with nonlinear dynamics under sensing range constraints. Since formation tracking alone does not ensure rigidity maintenance with a limited sensing range, despite rigidity being a prerequisite for establishing and preserving a unique formation, our work integrates both objectives through a single Control Barrier Function (CBF)-like constraint within a quadratic optimization framework. The proposed distributed controller requires only local relative information from neighbors, as verified with simulation case studies.
Control barrier functions (CBFs) provide a systematic framework for enforcing safety constraints in nonlinear control systems. However, their implementation typically relies on accurate system models, which can limit their applicability in the presence of significant modeling uncertainties or unknown dynamics. This paper proposes a model-free framework for the computation of recursive control barrier functions based on the ultra-local model approach that leverages online estimation of the unknown system dynamics to construct CBF constraints. This approach does not require an explicit model of the system dynamics and enhances robustness with respect to disturbances and model mismatch. The resulting control architecture enables the enforcement as well as the anticipation of safety constraints for systems with higher relative degree. The effectiveness of the proposed approach is illustrated on the adaptive cruise control benchmark.
Operating teams of autonomous aircraft in dynamic, uncertain, and potentially adversarial environments requires safety protocols that are reliable yet selective, and allow agents to fly in close proximity while making progress toward mission objectives. We introduce adversarial time-to-collision (aTTC), a risk metric that quantifies, for a given agent, how quickly any surrounding agent could reach it assuming adversarial intent. We embed aTTC into the control barrier function (CBF) framework, defining the barrier directly in time rather than distance or velocity. The resulting aTTC-CBF is inherently anticipatory: agents modulate their own velocity based not on whether a peer is on a collision course, but on how quickly one could reach collision given its dynamical constraints. A differentiable neural-network surrogate makes the aTTC computable in real time within a standard CBF quadratic program. Across long time-horizon simulations of 3D independent-pursuit and formation-flight scenarios, the aTTC-CBF achieves up to twice the waypoint progress at half the collision rate of a higher-order distance-based CBF baseline.
This paper presents a control barrier function-based method for real-time in-domain congestion control of the Lighthill-Whitham-Richards traffic model. Traffic congestion is formulated as a distributed safety control problem, leading to a infinite-dimensional optimization problem. Through the discretization and Karush-Kuhn-Tucker (KKT) analysis, the problem is converted into a high-dimensional quadratic program. A structure-exploiting primal-dual active set algorithm is then developed to compute the safe control input in real time, with convergence guarantees. Numerical simulations with different nominal controllers demonstrate the effectiveness and real-time feasibility of the proposed approach.
This paper studies safety analysis and controller synthesis for partially observable nonlinear control systems. We extend the control barrier--value function (CBVF) framework, which combines Hamilton--Jacobi reachability and control barrier functions, to settings where full state information is not available and control is based on an estimated state. Given an estimator, we apply conformal prediction to the estimation error and obtain an error bound at a user-chosen miscoverage level. We incorporate this bound into the estimator-space safety analysis and define a CBVF-based safety certificate for partially observable systems. We then derive a finite-horizon probabilistic safety guarantee for the true system state. Finally, we propose a QP-based online safety filter for systems affine in the control and disturbance, whose solution enforces the CBVF safety condition in real time against bounded disturbance. The proposed framework is illustrated on a partially observable obstacle-avoidance case study.
Fast charging of Lithium-ion batteries can lead to a significant temperature rise, which can cause serious risks to battery safety and lifetime. To ensure safe battery operation, thermal constraints must be enforced during the fast charging process. However, the core temperature of the battery cannot be directly measured in practice, which makes real-time safety enforcement challenging. This paper proposes a framework that incorporates core temperature estimates from Kolmogorov-Arnold Network within robust control barrier function (KAN-rCBF) constraints for battery fast-charging. The algorithm utilizes measurements from battery surface temperature, coolant temperature, coolant power, and charging current to solve a quadratic programming problem under safety constraints. We prescribe analytical safety guarantees for this optimal charging policy under KAN estimation errors and model uncertainty. Simulation results show that the proposed method maintains a safe battery temperature while achieving charging times comparable to the state-of-the-art method, where the latter fails to guarantee the same level of thermal safety.
We present a robust safety-filtering framework for input-constrained underactuated linear systems subject to unknown disturbances. A baseline H-$\infty$ input is derived from a zero-sum differential game, while a disturbance observer supplies an estimate and a transient error bound. The baseline input is adjusted using the disturbance estimate, while the estimate and its error bound are used to define robust high-order control barrier function constraints; forward invariance holds as long as the admissible-input set remains nonempty. For scalar-input systems, pointwise feasibility is determined from an exact input interval, and the interval width defines the feasibility margin. A finite-horizon H-$\infty$ performance balance accounts for the accumulated deviation of the applied input from the baseline H-$\infty$ policy. Simulations on a linearized two-wheeled balancing robot show how position and body-pitch constraints compete for the same bounded wheel-torque input.
Differentiable predictive control (DPC), a self-supervised learning approach for approximating explicit model predictive control (MPC) policies, offers significant computational advantages over online optimization-based MPC. However, feasibility guarantees, a core requirement for safe control, are currently provided either probabilistically or via online safety filters. The lack of rigorous feasibility guarantees for offline policy optimization remains an open problem. This paper establishes deterministic feasibility guarantees for DPC using a novel topological analysis of the induced reachable safe set, without requiring online safety filters. By exploiting the inherent model-based nature of DPC, in which differentiable system dynamics are embedded directly into the computational graph, we analyze the properties of the learned control policies and the corresponding system states from topological and geometric perspectives. Inspired by our theoretical analysis, we propose a novel self-supervised offline policy learning strategy that utilizes a proxy loss with Control Barrier Functions (CBFs). Crucially, these properties not only significantly improve policy training but also enable the derivation of strict, deterministic feasibility guarantees from a finite number of training samples. Extensive closed-loop simulations validate our theoretical findings, demonstrating that the empirical constraint violations monotonically decrease to zero as the training sample size increases. Ultimately, this work illustrates that DPC policy optimization yields formal safety certificates that are structurally unattainable with conventional black-box methods, e.g., reinforcement learning (RL) or supervised learning-based approximate MPC, thereby providing a new perspective on feasibility guarantees in learning-based control.
Safe actor-critic control often treats barrier filtering, uncertainty estimation, and experience replay as separate modules, even though each changes the data used for learning and control. We develop an integrated architecture in which the uncertainty estimate updates the obstacle geometry used by a control barrier function, filter interventions and estimation residuals determine replay priority, and the critic learns from the executed rather than nominal action. We instantiate the architecture on a two-dimensional robot-navigation task with corrupted obstacle measurements and compare six component-matched configurations under common training budgets, random seeds, sensor streams, exploration, and disturbances. Evaluation includes a moderate post-training test, an eleven-level perception-noise sweep, and an exploratory extreme-stress test at multiplier $6.0$. In the extreme test, the integrated configuration recorded no contacts and reached the goal in all five evaluation seeds. Its mean cost was $7.63\pm0.44$ and its obstacle-belief root-mean-square error was $3.52\pm0.55$ cm. The uncertainty-estimation ablation also recorded no contacts but reached the goal in four of five seeds, with mean cost $8.96\pm2.08$ and belief error $11.08\pm1.23$ cm. A finite-training bound clarifies replay exposure, and a robust barrier condition states the required estimation-error and feasibility assumptions. The results support coupling estimation, safety filtering, and replay on this benchmark; broader safety and convergence claims require further study.
Safely navigating polytopic environments while respecting the dynamics, control, and exact geometry of the underlying system is a challenge in robotics. Control barrier functions (CBFs) synthesize safe control policies by rendering the safe set forward invariant, but many existing CBF-based methods approximate polytopes using conservative smooth shapes, such as spheres or ellipsoids, to obtain explicit differentiable distance functions. In this article, we propose an exact Signed Distance Function (SDF) formulation for a {\it polytopic} robot and {\it polytopic} obstacles and integrate it with nonsmooth CBFs. Leveraging Minkowski operations, the proposed method computes the exact SDF via companion convex programs in both the collision-free (positive-sign) and in-collision (negative-sign) cases. Furthermore, by exploiting the convenient geometric properties of 2D Minkowski operations and the optimality conditions of the two companion convex programs, we derive a unified analytical expression for the gradient of the exact SDF via sensitivity analysis. The exact rotational gradient further reveals a previously masked class of local minima induced by the coupling between geometry and nonholonomic kinematics. We demonstrate the effectiveness of the proposed framework through a pure-translation case and three scenarios with unicycle models involving recovery from an unsafe initialization and single- and multiple-obstacle avoidance. Comparisons with baseline methods highlight how the proposed framework enables non-conservative maneuvers and safety recovery.
In vision-aided navigation and visual-inertial odometry, the quality of triangulated three-dimensional feature positions is a fundamental prerequisite for state estimation accuracy. Triangulation becomes ill-conditioned or even impossible when a camera undergoes pure rotation without translation, or when the observed bearing vectors provide insufficient parallax. Even though visual-inertial odometry has been extensively studied, the active maintenance of feature-observability during navigation has not been sufficiently addressed in the literature. To address this gap, this study presents TANGO-VIO, a triangulation-aware navigation framework that embeds a log-determinant metric of the feature-wise stacked-bearing matrix into a control barrier function. In this proposed method, the observability guarantee is established in the feature-geometric sense by enforcing a lower bound on the aggregate triangulation-information metric through a nominal-direction-weighted minimum-deviation velocity correction. The proposed architecture is evaluated through software-inthe- loop simulations and real flight experiments. The results show improved triangulation conditioning under low-parallax motion, while the flight response closely reproduces the corresponding simulation behavior and confirms the practical realizability of the proposed safety filter. Supplementary materials are available on the project webpage.
This article presents a modular inference framework that integrates Flow Matching generative models with formal Control Barrier Function (CBF) safety guarantees. Unlike existing methods that apply external safety filters to a model's final output, our approach modifies the Flow Matching denoising process within the model to inherently generate safe trajectories. By employing a smooth Log-Sum-Exponential aggregate barrier, we enforce safety over entire action chunks. This aggregate barrier ensures a minimal increase in computational overhead and does not alter the semantic intent of the model. We show that, within the proposed framework, the 2-Wasserstein distance between the generated distribution and the target distribution remains bounded. Our method eliminates the need for safety-specific datasets or costly model retraining, providing a versatile solution for safe inference. We validate the approach on two robotic manipulation platforms and a 2D navigation benchmark, verifying that our framework achieves reliable safety without degrading the success rate of the model.
Ensuring operation of aerospace systems within prescribed flight envelope limits is a fundamental requirement for modern flight control architectures. Flight envelope protection aims to prevent violations of aerodynamic and structural constraints, thereby mitigating risks such as stall and excessive load factors. Control barrier functions (CBFs) have emerged as a principled tool for enforcing safety by ensuring that the system state remains within a prescribed safe set. In most existing approaches, safety constraints are imposed at the control input-level based on an open-loop model of the system. While this open-loop model-based CBF formulation enables modular design, it may alter the closed-loop system dynamics, potentially compromising robustness guarantees and complicating integration into existing flight control architectures. This paper proposes a closed-loop model-based control barrier function (CLM-CBF) framework for flight envelope protection. The key idea is to enforce safety at the reference-level using an explicit model of the closed-loop system, thereby preserving the stability and robustness properties of the underlying controller. This formulation enables safety filtering without modifying the control law, facilitating modular integration and retrofitting into existing systems.
In this paper, a computationally lightweight approximate robust nonlinear model predictive control (NMPC) law is proposed based on a pair of input-to-state control Lyapunov function and robust control barrier function. The result builds upon and augments a recently introduced nominal infinitesimal- horizon NMPC scheme which permits small-sized quadratic programs to compute the feedback law for nonlinear constraint systems on embedded hardware in real time. Numerical experiments for nonlinear constrained spacecraft control and comparison to other robust NMPC schemes from the literature demonstrate the effectiveness of the proposed scheme.
This paper presents an adaptive safety-critical control framework for flight envelope protection (FEP) of hypersonic glide vehicles (HGVs) under model uncertainty. The proposed architecture treats input and state constraints through two complementary but distinct mechanisms. At the input end, an adaptive controller with a calibrated closed-loop reference model (CCRM) is designed to accommodate magnitude-limited control inputs and the effects of actuator saturation. Building on this input-constrained adaptive control architecture, flight envelope state constraints are enforced at the state end by an error-based safety filter (EBSF) based on control barrier functions (CBFs). The EBSF modifies the reference command and adapts the admissible safe set online using the measured mismatch between the reference model and the uncertain plant, thereby preserving forward invariance during transient adaptation. Simulation results for the DLR generic hypersonic glide vehicle 2 (GHGV-2) demonstrate stable, high-performance tracking under magnitude-limited control inputs while maintaining flight envelope constraints in the presence of model uncertainty.
We propose a notion of robust adaptive backup control barrier functions for nonlinear control affine systems with parametric uncertainty in both the drift dynamics and actuation matrix. Backup control barrier functions guarantee safety by predicting the system's trajectory under a pre-certified safe controller. However, these predictions rely on the model and can be inaccurate when the system contains unknown parameters. To address this issue, we estimate the unknown parameters using element-wise certified adaptive estimators that provide a parameter adaptation law and component-wise estimation error bounds. We compute the backup flow using the estimated model and tighten the safety conditions using these certified bounds. The resulting safety conditions account for the sensitivity of the predicted flow to parameter estimation errors. Moreover, to handle uncertainty in the actuation matrix, we use a duality-based reformulation that enables the use of a computationally efficient quadratic-program-based safety filter. We prove that controllers satisfying the proposed robust adaptive backup control barrier function constraints guarantee safety under parametric uncertainty and input constraints.
We consider the problem of learning high-dimensional semi-global feedback controllers under hard safety constraints enforced by control barrier functions (CBFs). Incorporating CBFs into end-to-end policy training requires embedding a quadratic-program-based safety filter as an optimization layer, but computational and differentiation bottlenecks have largely restricted prior approaches to low-dimensional systems, typically with at most 16 state dimensions. We address this limitation by combining operator splitting with the recently developed Jacobian-Free Backpropagation (JFB) method to enable scalable end-to-end training while preserving hard safety guarantees through the CBF safety filter. We justify this training methodology theoretically using nonsmooth analysis techniques and demonstrate its effectiveness on high-dimensional multi-agent nonlinear control problems with state and control dimensions up to 1200 and 400, respectively.
Multi-drone payload transportation has emerged as a promising research paradigm with potential applications in construction, logistics, and disaster response. However, the complex coupled dynamics among drones, cables, and payloads pose significant challenges, and existing approaches remain limited in safety and scalability, particularly in dynamic and unstructured environments. In this work, we propose a learning-based framework for safe and scalable multi-drone cooperative payload transport. We introduce a minimal 2D abstraction that preserves the task-relevant drone-payload coupling required for coordination and safety, while remaining computationally efficient for large-scale learning. Using domain randomization over team size and physical parameters, we train a fully distributed policy via Discrete Graph Control Barrier Function Proximal Policy Optimization (DGPPO), enabling robust zero-shot sim-to-real transfer without fine-tuning. Extensive real-world evaluations demonstrate that a single learned policy generalizes across varying team sizes and task scenarios. Furthermore, multi-group hardware experiments show that the same policy can safely operate in dynamic environments, where other drone teams act as moving obstacles. These results indicate that the proposed framework enables efficient, safe, and scalable multi-drone payload transportation with strong generalization to complex real-world conditions.
Long-reach drilling booms must reach successive poses without self-collision. Moving from operator-supervised control toward autonomy requires collision-aware motion planning and execution. For the Sandvik SB60, this study adapts established methods by integrating pose-parameterized planning with a capsule-based control barrier function quadratic program (CBF-QP) in measured-state inverse kinematics (IK). A fixed task-specific parameter set within each task generates waypoints, detours, timed references, and chained motion without target-specific retuning. The offline detour planner screens candidate waypoints using 23 selected rod-segment-to-body-region distances, whereas the online CBF-QP filters joint velocities using 14 configured capsule-pair constraints from a nine-primitive whole-body capsule model. Evaluation considers two drilling tasks in a manufacturer-developed SB60 Simscape Multibody model: a five-target restricted-orientation tour and a three-target full-pose tour. Across several hundred thousand samples, the method produced zero IK failures, generated several detour waypoints, achieved millimetre-level mean final-position error, and recorded no sampled CBF margins below the reported thresholds.
This paper investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next, we implement vector Lyapunov function approach to propose a novel high-order control Lyapunov function (HOCLF) for the stabilization control problem. The relations between the proposed and existing HOCBFs are discussed. Afterwards, the compatibility of the proposed HOCLF and HOCBF is addressed to guarantee the stabilization and safety control objectives simultaneously, and thus the optimal controller is established. Finally, a numerical example from the navigation problem of quadrotors is presented to illustrate the efficacy of the derived results.
Control barrier functions (CBFs) provide formal safety guarantees for constrained nonlinear systems, but their effectiveness relies on accurate system dynamics. In high-dimensional manipulators subject to unknown disturbances and model uncertainties, fixed safety constraints constructed from nominal dynamics may become inconsistent with the actual system behavior, leading to safety degradation or excessive conservatism. This paper proposes a dynamic constraint reconstruction based control barrier function (DCR-CBF) framework for safety-critical control of disturbed robotic manipulators. An extended state observer is employed to estimate lumped disturbances online, and the estimated disturbance is incorporated into high-order control barrier functions to reconstruct safety constraints according to the estimated true dynamics. To address estimation inaccuracies, a safety margin is introduced, and a sufficient condition is derived to guarantee forward invariance under bounded estimation errors. Simulation studies on a 4-DOF excavation manipulator demonstrate that the proposed DCR-CBF method achieves zero safety violation under strong unknown disturbances while significantly improving trajectory-tracking performance compared with standard and robust CBF methods.
Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by high-dimensional nonlinear dynamics, which presents challenges for model-based safety-critical control design. Motivated by the success of reduced-order models in robotics, this paper presents a tutorial on constructive safety-critical control via reduced-order models and control barrier functions (CBFs). To this end, we provide a unified formulation of techniques in the literature that share a common foundation of constructing CBFs for complex systems from CBFs for much simpler systems. Such ideas are illustrated through formal results, simple numerical examples, and case studies of real-world systems to which these techniques have been experimentally applied.
Balancing safety and performance is one of the predominant challenges in modern control system design. Moreover, it is crucial to robustly ensure safety without inducing unnecessary conservativeness that degrades performance. In this work, we present a constructive approach for safety-critical control synthesis via control barrier functions (CBFs). By filtering a hand-designed controller via a CBF, we are able to attain performant behavior while providing rigorous guarantees of safety. In the face of disturbances, robust safety and performance are simultaneously achieved through the notion of input-to-state safety (ISSf). We take a tutorial approach by developing the CBF-design methodology in parallel with an inverted pendulum example, making the challenges and sensitivities in the design process concrete. To establish the capability of the proposed approach, we consider the practical setting of safety-critical design via CBFs for a connected automated vehicle (CAV) in the form of a class-8 truck without a trailer. Through experimentation, we see the impact of unmodeled disturbances in the truck’s actuation system on the safety guarantees provided by CBFs. We characterize these disturbances and using ISSf, produce a robust controller that achieves safety without conceding performance. We evaluate our design both in simulation, and for the first time on an automotive system, experimentally.
Reinforcement Learning (RL) has been shown to be effective in many scenarios. However, it typically requires the exploration of a sufficiently large number of state-action pairs, some of which may be unsafe. Consequently, its application to safety-critical systems remains a challenge. An increasingly common approach to address safety involves the addition of a safety layer that projects the RL actions onto a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the safety layer to improve the learning performance. In this letter, we frame safety as a differentiable robust-control-barrier-function layer in a model-based RL framework. Moreover, we also propose an approach to modularly learn the underlying reward-driven task, independent of safety constraints. We demonstrate that this approach both ensures safety and effectively guides exploration during training in a range of experiments, including zero-shot transfer when the reward is learned in a constraint-agnostic fashion.
Obstacle avoidance between polytopes is a chal-lenging topic for optimal control and optimization-based tra-jectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simpli-fication of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control barrier function (DCBF) constraints and we propose a novel optimization formulation with dual variables based on DCBFs to generate a collision-free dynamically-feasible trajectory. The proposed optimization formulation has lower computational complexity compared to existing work and can be used as a fast online algorithm for control and planning for general nonlinear dynamical systems. We validate our algorithm on different robot shapes using numerical simulations with a kinematic bicycle model, resulting in successful navigation through maze environments with polytopic obstacles.
Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs). The limitations of these existing approaches are mainly about feasibility and safety. In the existing approaches, the feasibility of the optimization and the system safety cannot be enhanced at the same time theoretically. In this paper, we propose two formulations that unifies CLFs and CBFs under the framework of nonlinear model predictive control (NMPC). In the proposed formulations, safety criteria is commonly formulated as CBF constraints and stability performance is ensured with either a terminal cost function or CLF constraints. Slack variables with relaxing technique are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same. The advantages about feasibility and safety of proposed formulations compared with existing methods are analyzed theoretically and validated with numerical results.
While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive safety filters, which assess if a proposed learning-based control input can lead to constraint violations and modifies it if necessary to ensure safety for all future time steps. The theoretical guarantees of such predictive safety filters rely on the model assumptions and minor deviations can lead to failure of the filter putting the system at risk. This article introduces an auxiliary soft-constrained predictive control problem that is always feasible at each time step and asymptotically stabilizes the feasible set of the original predictive safety filter problem, thereby providing a recovery mechanism in safety–critical situations. This is achieved by a simple constraint tightening in combination with a terminal control barrier function. By extending discrete-time control barrier function theory, we establish that the proposed auxiliary problem provides a “predictive” control barrier function. The resulting algorithm is demonstrated using numerical examples.
The backup control barrier function (CBF) was recently proposed as a tractable formulation that guarantees the feasibility of the CBF quadratic programming (QP) via an implicitly defined control invariant set. The control invariant set is based on a fixed backup policy and evaluated online by forward integrating the dynamics under the backup policy. This paper is intended as a tutorial of the backup CBF approach and a comparative study to some benchmarks. First, the backup CBF approach is presented step by step with the underlying math explained in detail. Second, we prove that the backup CBF always has a relative degree 1 under mild assumptions. Third, the backup CBF approach is compared with benchmarks such as Hamilton Jacobi PDE and Sum-of-Squares on the computation of control invariant sets, which shows that one can obtain a control invariant set close to the maximum control invariant set under a good backup policy for many practical problems.
To bring complex systems into real world environments in a safe manner, they will have to be robust to uncertainties—both in the environment and the system. This letter investigates the safety of control systems under input disturbances, wherein the disturbances can capture uncertainties in the system. Safety, framed as forward invariance of sets in the state space, is ensured with the framework of control barrier functions (CBFs). Concretely, the definition of input-to-state safety (ISSf) is generalized to allow the synthesis of non-conservative, tunable controllers that are provably safe under varying disturbances. This is achieved by formulating the concept of tunable input-to-state safe control barrier functions (TISSf-CBFs), which guarantee safety for disturbances that vary with state and, therefore, provide less conservative means of accommodating uncertainty. The theoretical results are demonstrated with a simple control system with input disturbance and also applied to design a safe connected cruise controller for a heavy duty truck.
Artificial potential fields (APFs) and their variants have been a staple for collision avoidance of mobile robots and manipulators for almost 40 years. Its model-independent nature, ease of implementation, and real-time performance have played a large role in its continued success over the years. Control barrier functions (CBFs), on the other hand, are a more recent development, commonly used to guarantee safety for nonlinear systems in real-time in the form of a filter on a nominal controller. In this paper, we address the connections between APFs and CBFs. At a theoretic level, we show that given a broad class of APFs, one can construct a CBF that guarantees safety. Additionally, we prove that CBFs obtained from these APFs have additional beneficial properties and can be applied to nonlinear systems. Practically, we compare the performance of APFs and CBFs in the context of obstacle avoidance on simple illustrative examples and for a quadrotor with unknown dynamics, both in simulation and on hardware using onboard sensing.
In this paper, the issue of model uncertainty in safety-critical control is addressed with a data-driven approach. For this purpose, we utilize the structure of an input-ouput linearization controller based on a nominal model along with a Control Barrier Function and Control Lyapunov Function based Quadratic Program (CBF-CLF-QP). Specifically, we propose a novel reinforcement learning framework which learns the model uncertainty present in the CBF and CLF constraints, as well as other control-affine dynamic constraints in the quadratic program. The trained policy is combined with the nominal model-based CBF-CLF-QP, resulting in the Reinforcement Learning-based CBF-CLF-QP (RL-CBF-CLF-QP), which addresses the problem of model uncertainty in the safety constraints. The performance of the proposed method is validated by testing it on an underactuated nonlinear bipedal robot walking on randomly spaced stepping stones with one step preview, obtaining stable and safe walking under model uncertainty.
Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs). We consider the setting of a known nonlinear control affine dynamical system and assume that we have access to safe trajectories generated by an expert — a practical example of such a setting would be a kinematic model of a self-driving vehicle with safe trajectories (e.g., trajectories that avoid collisions with obstacles in the environment) generated by a human driver. We then propose and analyze an optimization based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz smoothness assumptions on the underlying dynamical system. A strength of our approach is that it is agnostic to the parameterization used to represent the CBF, assuming only that the Lipschitz constant of such functions can be efficiently bounded. Furthermore, if the CBF parameterization is convex, then under mild assumptions, so is our learning process. We end with extensive numerical evaluations of our results on both planar and realistic examples, using both random feature and deep neural network parameterizations of the CBF. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.
Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunov-based methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the system’s state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this unified framework to achieve stability and safety in an Adaptive Cruise Control (ACC) simulation.
This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.
This paper extends control barrier functions (CBFs) to high order control barrier functions (HOCBFs) that can be used for high relative degree constraints. The proposed HOCBFs are more general than recently proposed (exponential) HOCBFs. We introduce high order barrier functions (HOBFs), and show that their satisfaction of Lyapunov-like conditions implies the forward invariance of the intersection of a series of sets. We then introduce HOCBF, and show that any control input that satisfies the HOCBF constraint renders the intersection of a series of sets forward invariant. We formulate optimal control problems with constraints given by HOCBF and control Lyapunov functions (CLF), and provide a promising method to address the conflict between HOCBF constraints and control limitations by penalizing the class $\mathcal{K}$ functions. We illustrate the proposed method on an adaptive cruise control problem.
Abstract Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control. The extension of a barrier function to a controlled system results in a control barrier function. This can be thought of as being analogous to how Sontag extended Lyapunov functions to control Lypaunov functions in order to enable controller synthesis for stabilization tasks. A control barrier function enables controller synthesis for safety requirements specified by forward invariance of a set using a Lyapunov-like condition. This paper develops several important extensions to the notion of a control barrier function. The first involves robustness under perturbations to the vector field defining the system. Input-to-State stability conditions are given that provide for forward invariance, when disturbances are present, of a “relaxation” of set rendered invariant without disturbances. A control barrier function can be combined with a control Lyapunov function in a quadratic program to achieve a control objective subject to safety guarantees. The second result of the paper gives conditions for the control law obtained by solving the quadratic program to be Lipschitz continuous and therefore to gives rise to well-defined solutions of the resulting closed-loop system.
Robots navigating under occlusion may enter states from which no admissible input can avoid a dynamic obstacle once it becomes visible. We present OcclusionCBF, a safety filter that extends backup control barrier functions to reachable-occupancy predictions for potentially hidden dynamic obstacles in occluded regions. The method certifies a prescribed backup rollout against collision-inflated occupancy and a verified terminal set, yielding affine constraints for minimally invasive quadratic-program filtering. We establish recursive feasibility of the resulting safety filter, and collision avoidance for every hidden-obstacle motion covered by the occupancy prediction. Randomized benchmarks, MetaUrban simulations, and hardware experiments demonstrate improved task success over reactive and occlusion-aware predictive baselines with millisecond-scale computation.
The autonomous localization of fugitive gas emissions using small Unmanned Aircraft Systems (sUAS) constitutes a fundamentally ill-posed inverse problem. In turbulent atmospheric boundary layers, highly intermittent scalar concentration fields violate the assumptions of classical gradient-based navigation, causing data-driven estimators to suffer from severe noise and spurious local minima. To address these challenges, we introduce an Information-Guided Safe Reinforcement Learning framework evaluated within a custom, GPU-accelerated 3D simulation environment coupling an Eulerian wind solver with a Lagrangian puff dispersion model. We identify a critical vulnerability in deterministic information-seeking planners - a Gramian bias where agents act greedily upon flawed early estimates, starving the estimator of spatial diversity. To systematically break this degeneracy, our architecture integrates a classical empirical observability Gramian (EMGR) planner with a learned Soft Actor-Critic (SAC) exploratory policy. A deterministic meta-supervisor actively monitors estimator reliability via Kullback-Leibler (KL) divergence, dynamically blending deterministic exploitation with learned exploration to steer the sUAS into high-information zones. Trained via a progressive curriculum and safeguarded by a strictly enforced Robust Control Barrier Function (RCBF), our RL framework achieves nearly 80% localization success on complex, mobile sources - drastically outperforming classical baselines (~30%) - while ensuring zero safety violations.
Safety-aware motion planning remains a challenge in robotics, especially when missions are time-critical and are under complex specifications. In this paper, we propose safety-aware-stl-mppi, a computationally efficient sampling-based receding-horizon planning framework designed to promote satisfaction of constraints expressed in Signal Temporal Logic (STL). Our approach encodes discrete-time STL formulas into candidate time-varying control barrier functions (CBF), which are integrated into a model predictive path integral (MPPI) controller. Our method inherits the benefits of low computational cost from an efficiently parallelizable sampling based planner and utilizes CBF for constraints expressed in STL. We compare against several MPPI baselines using four artificial Mars Rover planning case studies with a diverse environment and cost setups, where we show our method consistently achieving high safety and efficiency. We show a quadcopter planning experiment with NVIDIA Isaac Lab.
This paper presents a safety-critical bilateral teleoperation framework for omnidirectional aerial manipulators that integrates visual and force-sensorless haptic wrench feedback. Unlike existing approaches that either rely on onboard force/torque sensors or use model-dependent wrench estimates, which may become unreliable under model uncertainties or induce unintended feedback during free-flight, our method implements a hierarchical safety filter based on control barrier functions to avoid such limitations. The safety filter, being the key contribution, explicitly accounts for tracking errors arising from physical interaction between the aerial manipulator and its surroundings while enforcing thrust limits, a factor overlooked despite its critical importance for flight safety. This safety filter adjusts the command from the operator to ensure safe and stable aerial manipulation and avoid motor saturation. The adjustment made by the filter is mapped to haptic feedback, which is intuitive to the operator and conveys information on physical interaction and impending motor saturation. By actual experiments with a hexarotor-based omnidirectional aerial manipulator, we demonstrate that the proposed method avoids haptic feedback during free-flight, provides directionally consistent feedback under physical interaction, and can be operated for diverse manipulative tasks. Moreover, an ablation study further shows that the saturation filter improves interaction stability by explicitly preventing motor saturation and informing the operator of corrective actions.
Safe and efficient shape-aware navigation in heterogeneous crowds and robot fleets remains challenging. Traditional approaches often assume homogeneous robots, sparse workspaces, simplified geometry, offline computation, or handcrafted parameters to make the problem tractable, which limits their deployment in dense crowd scenarios. Toward this end, we propose Shape-Aware Reinforcement Learned Model Predictive Control (SRL-MPC), a method for safe, efficient, and adaptive navigation in crowds with heterogeneous shapes without geometry simplification. To encode shape-aware safety, we formulate high-order control barrier function (HOCBF) constraints from geometric separation features (GSFs) based on support function transformation. A reinforcement learning (RL) framework then learns a neural policy that reads GSFs and outputs real-time MPC parameter updates, enabling the MPC solver to adapt to neighboring crowd geometries. The key advantage of SRL-MPC is that it preserves the safety structure and generalizability of MPC while integrating the adaptability and intelligence of RL. Experiments in randomized crowd scenarios with arbitrary shaped robot fleets demonstrate the effectiveness, scalability, and robustness of SRL-MPC. The results show that SRL-MPC substantially outperforms representative baselines in safety and adaptability. Project website: https://hanruihua.github.io/srl_mpc_project/
Safety filters are an effective tool for enforcing constraints in safety-critical systems, but most existing methods assume perfect state information, which is rarely available in practice. Recent work has begun to close this gap by developing filtering mechanisms that are robust to state estimation error, but these methods can still exhibit safety violations or overly conservative behavior as estimation error grows. Focusing on obstacle avoidance, we develop two new control barrier function (CBF) formulations: drift-measurement-robust (DMR)-CBFs and neural measurement-robust (NMR)-CBFs. The DMR-CBF augments the standard CBF condition with an inner optimization over the worst-case uncertainty in the drift dynamics, improving robustness to estimation error. This DMR-CBF then supervises a pretraining phase for the NMR-CBF, which replaces the inner optimization with a learned term. The NMR-CBF is subsequently finetuned through differentiable trajectory rollouts, yielding a filter that achieves empirical safety comparable to the DMR-CBF while reducing both conservativeness and computational cost. We provide theoretical analysis of the DMR-CBF along with numerical results on a planar double integrator and a 12D quadrotor, where both proposed approaches prevent collisions while other robust methods either fail or are overly conservative. Finally, we deployed the NMR-CBF on a Unitree Go2, enabling successful navigation of an obstacle field under odometry errors that caused a standard CBF to collide.
This paper presents a guide path-free multimodal trajectory planning framework for autonomous surface vehicles operating in dynamic environments. The proposed method integrates model predictive control (MPC) with a turning circle-based control barrier function (TC-CBF). Unlike conventional Euclidean distance-based CBFs (ED-CBFs), which evaluate safety solely based on proximity, the TC-CBF accounts for the nonholonomic motion and finite turning capability of a surface vehicle. Its geometric formulation identifies feasible avoidance regions according to the vehicle's turning circles and generates distinct left- and right-turning avoidance modes. These modes allow the optimization solver to explore and select topologically different trajectories without relying on globally planned guide paths, as required by many conventional multimodal planning approaches. By embedding the avoidance direction directly into the safety constraint, the proposed framework alleviates the local-minimum and deadlock problems of single-mode MPC while maintaining computational efficiency. Extensive simulations involving multiple moving vessels demonstrate that the proposed method achieves higher success rates, fewer safety violations, and smaller residual violations than single-mode baselines across all tested traffic densities.
Allocation schemes that greedily maximize a readiness metric over the actuator fiber bundle of an overactuated multirotor produce commands that jump between disconnected optimal strata, demanding actuator rates no motor can deliver; effort-minimizing schemes are continuous but cannot guarantee that wrench-rate authority stays above any certified level. We reconcile the two by treating authority as a forward-invariant quantity: a control barrier function on the log-determinant of the drag-aware actuator-authority co-metric, enforced at torque level by a quadratic program in the allocation null space. A single design inequality renders the certified set compact and strictly interior to the actuator box, with the readiness cost of any rotor deactivation given in closed form as $\ln(n/(n{-}m))$ for symmetric designs. Tracking is sacrificed only through an explicit alignment ratio, with wrench error bounded by $\mathcal{O}(ρ^{-1/2})$ and a robust variant handles motor-parameter uncertainty with a closed-form floor shift independent of the airframe matrix. On a hexarotor and a fully-actuated octorotor the closed-form gap matches simulation to machine precision; in the authority-scarce regime greedy maximization violates the certified floor and commits wrench errors up to eighty times larger than the proposed filter, which holds invariance of the certified set at negligible tracking cost.
Operating teams of autonomous aircraft in dynamic, uncertain, and potentially adversarial environments requires safety protocols that are reliable yet selective, and allow agents to fly in close proximity while making progress toward mission objectives. We introduce adversarial time-to-collision (aTTC), a risk metric that quantifies, for a given agent, how quickly any surrounding agent could reach it assuming adversarial intent. We embed aTTC into the control barrier function (CBF) framework, defining the barrier directly in time rather than distance or velocity. The resulting aTTC-CBF is inherently anticipatory: agents modulate their own velocity based not on whether a peer is on a collision course, but on how quickly one could reach collision given its dynamical constraints. A differentiable neural-network surrogate makes the aTTC computable in real time within a standard CBF quadratic program. Across long time-horizon simulations of 3D independent-pursuit and formation-flight scenarios, the aTTC-CBF achieves up to twice the waypoint progress at half the collision rate of a higher-order distance-based CBF baseline.
We present a robust safety-filtering framework for input-constrained underactuated linear systems subject to unknown disturbances. A baseline H-$\infty$ input is derived from a zero-sum differential game, while a disturbance observer supplies an estimate and a transient error bound. The baseline input is adjusted using the disturbance estimate, while the estimate and its error bound are used to define robust high-order control barrier function constraints; forward invariance holds as long as the admissible-input set remains nonempty. For scalar-input systems, pointwise feasibility is determined from an exact input interval, and the interval width defines the feasibility margin. A finite-horizon H-$\infty$ performance balance accounts for the accumulated deviation of the applied input from the baseline H-$\infty$ policy. Simulations on a linearized two-wheeled balancing robot show how position and body-pitch constraints compete for the same bounded wheel-torque input.
Reduced-order models based on Cosserat-rod theory are now well established, and modeling theory is no longer the primary bottleneck in soft-robot control. Their implementations, however, do not support the differentiable, GPU-parallel, and control-oriented workflows that underpin advanced rigid-robotics applications. Here, we fill this gap with SoRoMoX (Soft Robot Models in JAX), a fully numerical, JIT-compilable Python/JAX framework. SoRoMoX implements articulated, Piecewise Constant Strain, and Variable Strain models through a unified, control-ready interface that provides inertia matrices, gravitational and elastic forces, Jacobians, and their derivatives. To our knowledge, it is the first rod/strain-based soft-robot modeling framework that runs directly on GPUs and is end-to-end differentiable with respect to states, inputs, and parameters. Sequential CPU rollouts are up to 18.1x faster than state-of-the-art alternatives, while GPU-parallel rollouts increase throughput by up to 234.6x. This performance enables workflows that were previously impractical or impossible: static-equilibrium system identification with 66% lower marker RMSE; residual-force learning with a further 64% reduction; computed-torque tracking with RMSE reduced by a factor of approximately 500 relative to model-free PD; control-gain optimization with up to 62% lower loss than untuned gains; safety-constrained control using high-order control barrier functions to keep the peak contact force within a prescribed 5 N bound, compared with 33.5 N without the safety constraint; and reinforcement-learning policy training up to 7x faster than a CPU PyElastica discrete-rod baseline through massively parallel rollouts.
Safe actor-critic control often treats barrier filtering, uncertainty estimation, and experience replay as separate modules, even though each changes the data used for learning and control. We develop an integrated architecture in which the uncertainty estimate updates the obstacle geometry used by a control barrier function, filter interventions and estimation residuals determine replay priority, and the critic learns from the executed rather than nominal action. We instantiate the architecture on a two-dimensional robot-navigation task with corrupted obstacle measurements and compare six component-matched configurations under common training budgets, random seeds, sensor streams, exploration, and disturbances. Evaluation includes a moderate post-training test, an eleven-level perception-noise sweep, and an exploratory extreme-stress test at multiplier $6.0$. In the extreme test, the integrated configuration recorded no contacts and reached the goal in all five evaluation seeds. Its mean cost was $7.63\pm0.44$ and its obstacle-belief root-mean-square error was $3.52\pm0.55$ cm. The uncertainty-estimation ablation also recorded no contacts but reached the goal in four of five seeds, with mean cost $8.96\pm2.08$ and belief error $11.08\pm1.23$ cm. A finite-training bound clarifies replay exposure, and a robust barrier condition states the required estimation-error and feasibility assumptions. The results support coupling estimation, safety filtering, and replay on this benchmark; broader safety and convergence claims require further study.
Safely navigating polytopic environments while respecting the dynamics, control, and exact geometry of the underlying system is a challenge in robotics. Control barrier functions (CBFs) synthesize safe control policies by rendering the safe set forward invariant, but many existing CBF-based methods approximate polytopes using conservative smooth shapes, such as spheres or ellipsoids, to obtain explicit differentiable distance functions. In this article, we propose an exact Signed Distance Function (SDF) formulation for a {\it polytopic} robot and {\it polytopic} obstacles and integrate it with nonsmooth CBFs. Leveraging Minkowski operations, the proposed method computes the exact SDF via companion convex programs in both the collision-free (positive-sign) and in-collision (negative-sign) cases. Furthermore, by exploiting the convenient geometric properties of 2D Minkowski operations and the optimality conditions of the two companion convex programs, we derive a unified analytical expression for the gradient of the exact SDF via sensitivity analysis. The exact rotational gradient further reveals a previously masked class of local minima induced by the coupling between geometry and nonholonomic kinematics. We demonstrate the effectiveness of the proposed framework through a pure-translation case and three scenarios with unicycle models involving recovery from an unsafe initialization and single- and multiple-obstacle avoidance. Comparisons with baseline methods highlight how the proposed framework enables non-conservative maneuvers and safety recovery.
In vision-aided navigation and visual-inertial odometry, the quality of triangulated three-dimensional feature positions is a fundamental prerequisite for state estimation accuracy. Triangulation becomes ill-conditioned or even impossible when a camera undergoes pure rotation without translation, or when the observed bearing vectors provide insufficient parallax. Even though visual-inertial odometry has been extensively studied, the active maintenance of feature-observability during navigation has not been sufficiently addressed in the literature. To address this gap, this study presents TANGO-VIO, a triangulation-aware navigation framework that embeds a log-determinant metric of the feature-wise stacked-bearing matrix into a control barrier function. In this proposed method, the observability guarantee is established in the feature-geometric sense by enforcing a lower bound on the aggregate triangulation-information metric through a nominal-direction-weighted minimum-deviation velocity correction. The proposed architecture is evaluated through software-inthe- loop simulations and real flight experiments. The results show improved triangulation conditioning under low-parallax motion, while the flight response closely reproduces the corresponding simulation behavior and confirms the practical realizability of the proposed safety filter. Supplementary materials are available on the project webpage.
This article presents a modular inference framework that integrates Flow Matching generative models with formal Control Barrier Function (CBF) safety guarantees. Unlike existing methods that apply external safety filters to a model's final output, our approach modifies the Flow Matching denoising process within the model to inherently generate safe trajectories. By employing a smooth Log-Sum-Exponential aggregate barrier, we enforce safety over entire action chunks. This aggregate barrier ensures a minimal increase in computational overhead and does not alter the semantic intent of the model. We show that, within the proposed framework, the 2-Wasserstein distance between the generated distribution and the target distribution remains bounded. Our method eliminates the need for safety-specific datasets or costly model retraining, providing a versatile solution for safe inference. We validate the approach on two robotic manipulation platforms and a 2D navigation benchmark, verifying that our framework achieves reliable safety without degrading the success rate of the model.
Multi-drone payload transportation has emerged as a promising research paradigm with potential applications in construction, logistics, and disaster response. However, the complex coupled dynamics among drones, cables, and payloads pose significant challenges, and existing approaches remain limited in safety and scalability, particularly in dynamic and unstructured environments. In this work, we propose a learning-based framework for safe and scalable multi-drone cooperative payload transport. We introduce a minimal 2D abstraction that preserves the task-relevant drone-payload coupling required for coordination and safety, while remaining computationally efficient for large-scale learning. Using domain randomization over team size and physical parameters, we train a fully distributed policy via Discrete Graph Control Barrier Function Proximal Policy Optimization (DGPPO), enabling robust zero-shot sim-to-real transfer without fine-tuning. Extensive real-world evaluations demonstrate that a single learned policy generalizes across varying team sizes and task scenarios. Furthermore, multi-group hardware experiments show that the same policy can safely operate in dynamic environments, where other drone teams act as moving obstacles. These results indicate that the proposed framework enables efficient, safe, and scalable multi-drone payload transportation with strong generalization to complex real-world conditions.
Aquatic self-reconfigurable robots must assemble into desired shapes while ensuring safe interactions among multiple agents. This paper proposes a hybrid framework that combines distributed Model Predictive Control (MPC) with Control Barrier Functions (CBFs) for multi-agent shape formation and reconfiguration. Given a desired shape and target assignment, a distributed MPC scheme, solved via the Alternating Direction Method of Multipliers (ADMM), computes coordinated trajectories through local optimization and information exchange. To ensure safety in real time, distributed CBF-based filters are applied to enforce inter-agent collision avoidance. The proposed approach leverages the predictive capabilities of MPC to mitigate local minima, while CBFs provide formal safety guarantees despite the nonconvexity of the underlying optimization problem. Simulation results with up to 25 agents and experimental validation with four physical robots demonstrate the effectiveness and scalability of the framework.
Haptic feedback provides an implicit channel for communicating safety intentions during human-robot shared control. Existing haptic guidance systems typically employ predefined intervention strategies that cannot accommodate the diverse safety preferences of individual users or application scenarios. To address this limitation, we propose a Learning from Haptics (LfH) framework that learns user-preferred safety interventions from sparse demonstrations, eliminating the need for manual trial-and-error design. Our framework is built on a differentiable Control Barrier Function (CBF)-based optimization layer that automatically adjusts the underlying safety parameters to match the demonstrated haptic responses. Instead of tuning controller parameters directly, users teach the system how they expect it to intervene during teleoperation. The resulting haptic guidance reflects the demonstrated intervention preferences while preserving the intuitive interaction of haptic shared control. Simulation and hardware experiments demonstrate that the proposed framework can learn personalized safety interventions from sparse user input and reduce the mismatch between the generated haptic feedback and the demonstrated preferences.
Long-reach drilling booms must reach successive poses without self-collision. Moving from operator-supervised control toward autonomy requires collision-aware motion planning and execution. For the Sandvik SB60, this study adapts established methods by integrating pose-parameterized planning with a capsule-based control barrier function quadratic program (CBF-QP) in measured-state inverse kinematics (IK). A fixed task-specific parameter set within each task generates waypoints, detours, timed references, and chained motion without target-specific retuning. The offline detour planner screens candidate waypoints using 23 selected rod-segment-to-body-region distances, whereas the online CBF-QP filters joint velocities using 14 configured capsule-pair constraints from a nine-primitive whole-body capsule model. Evaluation considers two drilling tasks in a manufacturer-developed SB60 Simscape Multibody model: a five-target restricted-orientation tour and a three-target full-pose tour. Across several hundred thousand samples, the method produced zero IK failures, generated several detour waypoints, achieved millimetre-level mean final-position error, and recorded no sampled CBF margins below the reported thresholds.
This paper investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next, we implement vector Lyapunov function approach to propose a novel high-order control Lyapunov function (HOCLF) for the stabilization control problem. The relations between the proposed and existing HOCBFs are discussed. Afterwards, the compatibility of the proposed HOCLF and HOCBF is addressed to guarantee the stabilization and safety control objectives simultaneously, and thus the optimal controller is established. Finally, a numerical example from the navigation problem of quadrotors is presented to illustrate the efficacy of the derived results.
This paper presents a safety-critical distributed nonlinear model predictive control (DNMPC) framework for cooperative payload transportation by teams of quadrupedal robots. The proposed approach models the robotic team and the shared payload as a dynamically coupled networked system with rigid holonomic coupling constraints arising from cooperative transportation. To enable distributed real-time optimization, the centralized finite-horizon optimal control problem is decomposed into parallel local NMPC subproblems coordinated through the alternating direction method of multipliers (ADMM). The resulting distributed framework enforces consensus over both payload-state and interaction-wrench trajectories while explicitly incorporating acceleration-level holonomic coupling constraints within the distributed predictive control formulation. Safety-critical obstacle avoidance constraints for both the robotic agents and payload are enforced using higher-order control barrier functions (HOCBFs). The framework is validated through numerical simulations with teams of two, three, and four quadrupedal robots transporting shared payloads in cluttered environments. Real-time experiments on two- and three-robot teams demonstrate safe and robust transportation under payload uncertainty and external disturbances. Compared with centralized NMPC, the proposed framework achieves up to 23% reduction in average NLP solve time while maintaining comparable closed-loop performance. Ablation studies further demonstrate robustness to communication delays and show that explicit payload-state consensus and holonomic constraints substantially improve payload tracking and distributed coordination over existing wrench-only consensus formulations.
Autonomous rendezvous and proximity operations (RPO) in adversarial orbital environments require guidance architectures balancing target pursuit, safety preservation, and real-time adaptability under dynamically evolving interaction conditions. Although learning-based approaches show promise, their application to safety-critical orbital robotics remains limited by concerns regarding interpretability, robustness, and constraint awareness. This work presents an adaptive Model Predictive Control (MPC) framework for autonomous spacecraft RPO in multi-agent adversarial scenarios. The proposed architecture combines a constrained receding-horizon MPC formulation with a data-driven supervisory tuning layer that adjusts controller parameters from offline closed-loop evaluation and online interaction geometry. Relative motion follows Clohessy-Wiltshire (CW) dynamics, enabling computationally efficient finite-horizon prediction and real-time quadratic optimization. The MPC formulation incorporates actuator limits, predictive keep-out-zone constraints, slack-variable feasibility handling, and optional Control Barrier Function (CBF) safety filtering. Rather than generating thrust commands directly, the adaptive layer modifies interpretable MPC parameters, including tracking weights, safety penalties, minimum-separation objectives, and keep-out-zone objectives. The framework was evaluated in the official Kerbal Space Program Differential Game (KSPDG) Capture-the-Satellite environment through Monte Carlo simulations. Results demonstrate improved closed-loop robustness, adaptive maneuvering behavior, and rendezvous performance compared with fixed-parameter MPC while preserving safety-aware operation and real-time feasibility, providing a modular, interpretable foundation for adaptive spacecraft RPO.
Safe model-based reinforcement learning (RL) often bridges control-theoretic analysis and RL for robots to safely explore (partially) unknown system dynamics while deriving control actions for task efficiency. The control performance and safety assurance typically rely on prior knowledge of partially modeled nominal system dynamics and the data-driven models that compensate for residual model uncertainties. However, existing methods often overlook the structure of residual model uncertainties (e.g., components affine in control), which could lead to overly conservative robot behaviors or invalid safety guarantees under the safe learning-based controllers. This paper proposes a safe reinforcement learning framework that learns control-affine dynamics with a certifiable data-driven safe policy using control barrier functions (CBF). Specifically, we first use Control-Affine Random Fourier Features (ARFF) to model robot dynamics in a control-affine form, which offers computational efficiency that scales with dataset size and reduces potential model bias for model-based reinforcement learning. Then, a model-free, efficient uncertainty quantification method using adaptive conformal prediction (ACP) is applied to quantify the uncertainty in the safety constraint arising from the learned control-affine dynamics. This allows for data-driven safety assurance amenable to principled and efficient controller synthesis with CBF. Simulation results on the cartpole and the 3D quadrotor platforms demonstrate the effectiveness of the proposed framework.
Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by high-dimensional nonlinear dynamics, which presents challenges for model-based safety-critical control design. Motivated by the success of reduced-order models in robotics, this paper presents a tutorial on constructive safety-critical control via reduced-order models and control barrier functions (CBFs). To this end, we provide a unified formulation of techniques in the literature that share a common foundation of constructing CBFs for complex systems from CBFs for much simpler systems. Such ideas are illustrated through formal results, simple numerical examples, and case studies of real-world systems to which these techniques have been experimentally applied.
Balancing safety and performance is one of the predominant challenges in modern control system design. Moreover, it is crucial to robustly ensure safety without inducing unnecessary conservativeness that degrades performance. In this work, we present a constructive approach for safety-critical control synthesis via control barrier functions (CBFs). By filtering a hand-designed controller via a CBF, we are able to attain performant behavior while providing rigorous guarantees of safety. In the face of disturbances, robust safety and performance are simultaneously achieved through the notion of input-to-state safety (ISSf). We take a tutorial approach by developing the CBF-design methodology in parallel with an inverted pendulum example, making the challenges and sensitivities in the design process concrete. To establish the capability of the proposed approach, we consider the practical setting of safety-critical design via CBFs for a connected automated vehicle (CAV) in the form of a class-8 truck without a trailer. Through experimentation, we see the impact of unmodeled disturbances in the truck’s actuation system on the safety guarantees provided by CBFs. We characterize these disturbances and using ISSf, produce a robust controller that achieves safety without conceding performance. We evaluate our design both in simulation, and for the first time on an automotive system, experimentally.
Reinforcement Learning (RL) has been shown to be effective in many scenarios. However, it typically requires the exploration of a sufficiently large number of state-action pairs, some of which may be unsafe. Consequently, its application to safety-critical systems remains a challenge. An increasingly common approach to address safety involves the addition of a safety layer that projects the RL actions onto a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the safety layer to improve the learning performance. In this letter, we frame safety as a differentiable robust-control-barrier-function layer in a model-based RL framework. Moreover, we also propose an approach to modularly learn the underlying reward-driven task, independent of safety constraints. We demonstrate that this approach both ensures safety and effectively guides exploration during training in a range of experiments, including zero-shot transfer when the reward is learned in a constraint-agnostic fashion.
Obstacle avoidance between polytopes is a chal-lenging topic for optimal control and optimization-based tra-jectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simpli-fication of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control barrier function (DCBF) constraints and we propose a novel optimization formulation with dual variables based on DCBFs to generate a collision-free dynamically-feasible trajectory. The proposed optimization formulation has lower computational complexity compared to existing work and can be used as a fast online algorithm for control and planning for general nonlinear dynamical systems. We validate our algorithm on different robot shapes using numerical simulations with a kinematic bicycle model, resulting in successful navigation through maze environments with polytopic obstacles.
Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs). The limitations of these existing approaches are mainly about feasibility and safety. In the existing approaches, the feasibility of the optimization and the system safety cannot be enhanced at the same time theoretically. In this paper, we propose two formulations that unifies CLFs and CBFs under the framework of nonlinear model predictive control (NMPC). In the proposed formulations, safety criteria is commonly formulated as CBF constraints and stability performance is ensured with either a terminal cost function or CLF constraints. Slack variables with relaxing technique are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same. The advantages about feasibility and safety of proposed formulations compared with existing methods are analyzed theoretically and validated with numerical results.
Artificial potential fields (APFs) and their variants have been a staple for collision avoidance of mobile robots and manipulators for almost 40 years. Its model-independent nature, ease of implementation, and real-time performance have played a large role in its continued success over the years. Control barrier functions (CBFs), on the other hand, are a more recent development, commonly used to guarantee safety for nonlinear systems in real-time in the form of a filter on a nominal controller. In this paper, we address the connections between APFs and CBFs. At a theoretic level, we show that given a broad class of APFs, one can construct a CBF that guarantees safety. Additionally, we prove that CBFs obtained from these APFs have additional beneficial properties and can be applied to nonlinear systems. Practically, we compare the performance of APFs and CBFs in the context of obstacle avoidance on simple illustrative examples and for a quadrotor with unknown dynamics, both in simulation and on hardware using onboard sensing.
In this paper, the issue of model uncertainty in safety-critical control is addressed with a data-driven approach. For this purpose, we utilize the structure of an input-ouput linearization controller based on a nominal model along with a Control Barrier Function and Control Lyapunov Function based Quadratic Program (CBF-CLF-QP). Specifically, we propose a novel reinforcement learning framework which learns the model uncertainty present in the CBF and CLF constraints, as well as other control-affine dynamic constraints in the quadratic program. The trained policy is combined with the nominal model-based CBF-CLF-QP, resulting in the Reinforcement Learning-based CBF-CLF-QP (RL-CBF-CLF-QP), which addresses the problem of model uncertainty in the safety constraints. The performance of the proposed method is validated by testing it on an underactuated nonlinear bipedal robot walking on randomly spaced stepping stones with one step preview, obtaining stable and safe walking under model uncertainty.
This paper extends control barrier functions (CBFs) to high order control barrier functions (HOCBFs) that can be used for high relative degree constraints. The proposed HOCBFs are more general than recently proposed (exponential) HOCBFs. We introduce high order barrier functions (HOBFs), and show that their satisfaction of Lyapunov-like conditions implies the forward invariance of the intersection of a series of sets. We then introduce HOCBF, and show that any control input that satisfies the HOCBF constraint renders the intersection of a series of sets forward invariant. We formulate optimal control problems with constraints given by HOCBF and control Lyapunov functions (CLF), and provide a promising method to address the conflict between HOCBF constraints and control limitations by penalizing the class $\mathcal{K}$ functions. We illustrate the proposed method on an adaptive cruise control problem.
In this paper, we consider generalized Nash equilibrium (GNE) seeking in non-cooperative games with coupled constraint sets. Specifically, we aim to enforce safety for distributed GNE seeking, whereby the safety specifications are encoded in the coupled constraint set. To achieve this, we introduce the control barrier function (CBF) in the design of the GNE seeking dynamics. We design the dynamics for both full- and partial-information setting, where each player has knowledge of the decision information of all other players or only neighboring players, respectively. We justify the proposed dynamics by showing that the coupled constraint set is forward invariant, the equilibrium of the dynamics coincides with the exact GNE of the game, and the dynamics is asymptotically stable. Furthermore, we extend the approach to games where the agents are multi-integrators. Numerical simulations are provided to verify our results.
Allocation schemes that greedily maximize a readiness metric over the actuator fiber bundle of an overactuated multirotor produce commands that jump between disconnected optimal strata, demanding actuator rates no motor can deliver; effort-minimizing schemes are continuous but cannot guarantee that wrench-rate authority stays above any certified level. We reconcile the two by treating authority as a forward-invariant quantity: a control barrier function on the log-determinant of the drag-aware actuator-authority co-metric, enforced at torque level by a quadratic program in the allocation null space. A single design inequality renders the certified set compact and strictly interior to the actuator box, with the readiness cost of any rotor deactivation given in closed form as $\ln(n/(n{-}m))$ for symmetric designs. Tracking is sacrificed only through an explicit alignment ratio, with wrench error bounded by $\mathcal{O}(ρ^{-1/2})$ and a robust variant handles motor-parameter uncertainty with a closed-form floor shift independent of the airframe matrix. On a hexarotor and a fully-actuated octorotor the closed-form gap matches simulation to machine precision; in the authority-scarce regime greedy maximization violates the certified floor and commits wrench errors up to eighty times larger than the proposed filter, which holds invariance of the certified set at negligible tracking cost.
Control barrier functions (CBFs) provide a systematic framework for enforcing safety constraints in nonlinear control systems. However, their implementation typically relies on accurate system models, which can limit their applicability in the presence of significant modeling uncertainties or unknown dynamics. This paper proposes a model-free framework for the computation of recursive control barrier functions based on the ultra-local model approach that leverages online estimation of the unknown system dynamics to construct CBF constraints. This approach does not require an explicit model of the system dynamics and enhances robustness with respect to disturbances and model mismatch. The resulting control architecture enables the enforcement as well as the anticipation of safety constraints for systems with higher relative degree. The effectiveness of the proposed approach is illustrated on the adaptive cruise control benchmark.
Operating teams of autonomous aircraft in dynamic, uncertain, and potentially adversarial environments requires safety protocols that are reliable yet selective, and allow agents to fly in close proximity while making progress toward mission objectives. We introduce adversarial time-to-collision (aTTC), a risk metric that quantifies, for a given agent, how quickly any surrounding agent could reach it assuming adversarial intent. We embed aTTC into the control barrier function (CBF) framework, defining the barrier directly in time rather than distance or velocity. The resulting aTTC-CBF is inherently anticipatory: agents modulate their own velocity based not on whether a peer is on a collision course, but on how quickly one could reach collision given its dynamical constraints. A differentiable neural-network surrogate makes the aTTC computable in real time within a standard CBF quadratic program. Across long time-horizon simulations of 3D independent-pursuit and formation-flight scenarios, the aTTC-CBF achieves up to twice the waypoint progress at half the collision rate of a higher-order distance-based CBF baseline.
Control barrier functions (CBFs) have become an important controller design tool for autonomous systems subject to safety constraints. Despite their popularity, recent works have shown that CBF-based controllers can destabilize the internal dynamics of the system. In this paper, we consider linear systems with affine safety constraints and design linear feedback controllers that satisfy high-order CBF (HOCBF) constraints while rendering the origin globally exponentially stable. We first characterize the exact class of all linear gain matrices that globally satisfy the HOCBF constraints, including necessary and sufficient conditions for when this class is nonempty. Then, by leveraging the recently introduced notion of CBF output dynamics and CBF internal dynamics, we provide the necessary and sufficient conditions for the existence of stabilizing gain matrices within that class. Finally, we show that Linear Quadratic Regulator (LQR) and robust control problems can be solved while being constrained within this class of safe and stabilizing gain matrices, through standard linear control techniques such as algebraic Riccati equations (AREs) and Linear Matrix Inequalities (LMIs). We illustrate our results in a simulation example.
We consider the problem of learning high-dimensional semi-global feedback controllers under hard safety constraints enforced by control barrier functions (CBFs). Incorporating CBFs into end-to-end policy training requires embedding a quadratic-program-based safety filter as an optimization layer, but computational and differentiation bottlenecks have largely restricted prior approaches to low-dimensional systems, typically with at most 16 state dimensions. We address this limitation by combining operator splitting with the recently developed Jacobian-Free Backpropagation (JFB) method to enable scalable end-to-end training while preserving hard safety guarantees through the CBF safety filter. We justify this training methodology theoretically using nonsmooth analysis techniques and demonstrate its effectiveness on high-dimensional multi-agent nonlinear control problems with state and control dimensions up to 1200 and 400, respectively.
This paper presents a safety-critical distributed nonlinear model predictive control (DNMPC) framework for cooperative payload transportation by teams of quadrupedal robots. The proposed approach models the robotic team and the shared payload as a dynamically coupled networked system with rigid holonomic coupling constraints arising from cooperative transportation. To enable distributed real-time optimization, the centralized finite-horizon optimal control problem is decomposed into parallel local NMPC subproblems coordinated through the alternating direction method of multipliers (ADMM). The resulting distributed framework enforces consensus over both payload-state and interaction-wrench trajectories while explicitly incorporating acceleration-level holonomic coupling constraints within the distributed predictive control formulation. Safety-critical obstacle avoidance constraints for both the robotic agents and payload are enforced using higher-order control barrier functions (HOCBFs). The framework is validated through numerical simulations with teams of two, three, and four quadrupedal robots transporting shared payloads in cluttered environments. Real-time experiments on two- and three-robot teams demonstrate safe and robust transportation under payload uncertainty and external disturbances. Compared with centralized NMPC, the proposed framework achieves up to 23% reduction in average NLP solve time while maintaining comparable closed-loop performance. Ablation studies further demonstrate robustness to communication delays and show that explicit payload-state consensus and holonomic constraints substantially improve payload tracking and distributed coordination over existing wrench-only consensus formulations.
Obstacle avoidance between polytopes is a chal-lenging topic for optimal control and optimization-based tra-jectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simpli-fication of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control barrier function (DCBF) constraints and we propose a novel optimization formulation with dual variables based on DCBFs to generate a collision-free dynamically-feasible trajectory. The proposed optimization formulation has lower computational complexity compared to existing work and can be used as a fast online algorithm for control and planning for general nonlinear dynamical systems. We validate our algorithm on different robot shapes using numerical simulations with a kinematic bicycle model, resulting in successful navigation through maze environments with polytopic obstacles.
Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs). The limitations of these existing approaches are mainly about feasibility and safety. In the existing approaches, the feasibility of the optimization and the system safety cannot be enhanced at the same time theoretically. In this paper, we propose two formulations that unifies CLFs and CBFs under the framework of nonlinear model predictive control (NMPC). In the proposed formulations, safety criteria is commonly formulated as CBF constraints and stability performance is ensured with either a terminal cost function or CLF constraints. Slack variables with relaxing technique are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same. The advantages about feasibility and safety of proposed formulations compared with existing methods are analyzed theoretically and validated with numerical results.
The backup control barrier function (CBF) was recently proposed as a tractable formulation that guarantees the feasibility of the CBF quadratic programming (QP) via an implicitly defined control invariant set. The control invariant set is based on a fixed backup policy and evaluated online by forward integrating the dynamics under the backup policy. This paper is intended as a tutorial of the backup CBF approach and a comparative study to some benchmarks. First, the backup CBF approach is presented step by step with the underlying math explained in detail. Second, we prove that the backup CBF always has a relative degree 1 under mild assumptions. Third, the backup CBF approach is compared with benchmarks such as Hamilton Jacobi PDE and Sum-of-Squares on the computation of control invariant sets, which shows that one can obtain a control invariant set close to the maximum control invariant set under a good backup policy for many practical problems.
Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs). We consider the setting of a known nonlinear control affine dynamical system and assume that we have access to safe trajectories generated by an expert — a practical example of such a setting would be a kinematic model of a self-driving vehicle with safe trajectories (e.g., trajectories that avoid collisions with obstacles in the environment) generated by a human driver. We then propose and analyze an optimization based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz smoothness assumptions on the underlying dynamical system. A strength of our approach is that it is agnostic to the parameterization used to represent the CBF, assuming only that the Lipschitz constant of such functions can be efficiently bounded. Furthermore, if the CBF parameterization is convex, then under mild assumptions, so is our learning process. We end with extensive numerical evaluations of our results on both planar and realistic examples, using both random feature and deep neural network parameterizations of the CBF. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.
Control Barrier Functions (CBFs) aim to ensure safety by constraining the control input at each time step so that the system state remains within a desired safe region. This paper presents a framework for CBFs in stochastic systems in the presence of Gaussian process and measurement noise. We first consider the case where the system state is known at each time step, and present reciprocal and zero CBF constructions that guarantee safety with probability 1. We extend our results to high relative degree systems with linear dynamics and affine safety constraints. We then develop CBFs for incomplete state information environments, in which the state must be estimated using sensors that are corrupted by Gaussian noise. We prove that our proposed CBF ensures safety with probability 1 when the state estimate is within a given bound of the true state, which can be achieved using an Extended Kalman Filter when the system is linear or the process and measurement noise are sufficiently small. We propose control policies that combine these CBFs with Control Lyapunov Functions in order to jointly ensure safety and stochastic stability. Our results are validated via numerical study on an adaptive cruise control example.
This letter presents a new notion of input-to-state safe control barrier functions (ISSf-CBFs), which ensure safety of nonlinear dynamical systems under input disturbances. Similar to how safety conditions are specified in terms of forward invariance of a set, input-to-state safety conditions are specified in terms of forward invariance of a slightly larger set. In this context, invariance of the larger set implies that the states stay either inside or very close to the smaller safe set; and this closeness is bounded by the magnitude of the disturbances. The main contribution of the letter is the methodology used for obtaining a valid ISSf-CBF, given a control barrier function. The associated universal control law will also be provided. Towards the end, we will study unified quadratic programs that combine control Lyapunov functions and ISSf-CBFs in order to obtain a single control law that ensures both safety and stability in systems with input disturbances.
Abstract Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control. The extension of a barrier function to a controlled system results in a control barrier function. This can be thought of as being analogous to how Sontag extended Lyapunov functions to control Lypaunov functions in order to enable controller synthesis for stabilization tasks. A control barrier function enables controller synthesis for safety requirements specified by forward invariance of a set using a Lyapunov-like condition. This paper develops several important extensions to the notion of a control barrier function. The first involves robustness under perturbations to the vector field defining the system. Input-to-State stability conditions are given that provide for forward invariance, when disturbances are present, of a “relaxation” of set rendered invariant without disturbances. A control barrier function can be combined with a control Lyapunov function in a quadratic program to achieve a control objective subject to safety guarantees. The second result of the paper gives conditions for the control law obtained by solving the quadratic program to be Lipschitz continuous and therefore to gives rise to well-defined solutions of the resulting closed-loop system.
Mission-critical intelligent systems often operate under time-varying limitations that reduce control authority and change the admissible safe operating envelope. In such settings, a safety certificate learned under nominal conditions may become invalid as system capability changes. To address this challenge, this paper proposes a degradation-aware, data-driven safety-filtering framework that learns a safe set from data, updates it online, and enforces the resulting learned barrier through a time-varying control barrier function (CBF). A nominal safe envelope is first learned from operational data using a radial basis function (RBF)-kernel support vector machine (SVM), whose decision function serves as the initial CBF candidate. To capture capability-induced safe-set contraction, a continuous-time decremental SVM update law is developed so that selected support-vector coefficients are reduced according to a degradation signal. A homotopy-smoothed SVM-CBF is then introduced to avoid discontinuous changes in the learned barrier during active-set transitions. The resulting time-varying learned barrier is enforced using a quadratic-program-based safety filter under degraded input constraints. Forward invariance of the learned time-varying safe set and recursive feasibility of the safety filter are established. Simulation results on a vertical takeoff and landing (VTOL) model show that the proposed method maintains safety under reduced control authority and avoids abrupt barrier-switching effects during safe-set contraction.
Designing effective trading strategies using reinforcement learning remains challenging due to delayed and noisy rewards, poor exploration, and the difficulty of enforcing explicit risk constraints. In this work, we propose BRaG, a barycenter-based adversarial inverse reinforcement learning framework for stock trading that learns trading behavior from multiple heterogeneous expert strategies. BRaG aggregates expert demonstrations using a performance-weighted Wasserstein barycenter, yielding a stable pseudo-expert representation that captures shared structure across diverse trading styles. This representation is used to pretrain a trading policy via adversarial imitation learning, which alleviates unstable exploration during reinforcement learning. The pretrained policy is subsequently refined using reinforcement learning with true market rewards. To ensure risk-aware decision-making, BRaG incorporates control barrier functions that constrain action execution and regularize policy learning to satisfy drawdown limits. We evaluate the proposed approach on four major global equity markets, including the US, UK, Indian, and Taiwanese indices. Across all the markets, the proposed approach achieves stronger performance than both classical trading rules and recent deep reinforcement learning methods, while exhibiting more stable risk characteristics.
Differentiable predictive control (DPC), a self-supervised learning approach for approximating explicit model predictive control (MPC) policies, offers significant computational advantages over online optimization-based MPC. However, feasibility guarantees, a core requirement for safe control, are currently provided either probabilistically or via online safety filters. The lack of rigorous feasibility guarantees for offline policy optimization remains an open problem. This paper establishes deterministic feasibility guarantees for DPC using a novel topological analysis of the induced reachable safe set, without requiring online safety filters. By exploiting the inherent model-based nature of DPC, in which differentiable system dynamics are embedded directly into the computational graph, we analyze the properties of the learned control policies and the corresponding system states from topological and geometric perspectives. Inspired by our theoretical analysis, we propose a novel self-supervised offline policy learning strategy that utilizes a proxy loss with Control Barrier Functions (CBFs). Crucially, these properties not only significantly improve policy training but also enable the derivation of strict, deterministic feasibility guarantees from a finite number of training samples. Extensive closed-loop simulations validate our theoretical findings, demonstrating that the empirical constraint violations monotonically decrease to zero as the training sample size increases. Ultimately, this work illustrates that DPC policy optimization yields formal safety certificates that are structurally unattainable with conventional black-box methods, e.g., reinforcement learning (RL) or supervised learning-based approximate MPC, thereby providing a new perspective on feasibility guarantees in learning-based control.
We consider the problem of learning high-dimensional semi-global feedback controllers under hard safety constraints enforced by control barrier functions (CBFs). Incorporating CBFs into end-to-end policy training requires embedding a quadratic-program-based safety filter as an optimization layer, but computational and differentiation bottlenecks have largely restricted prior approaches to low-dimensional systems, typically with at most 16 state dimensions. We address this limitation by combining operator splitting with the recently developed Jacobian-Free Backpropagation (JFB) method to enable scalable end-to-end training while preserving hard safety guarantees through the CBF safety filter. We justify this training methodology theoretically using nonsmooth analysis techniques and demonstrate its effectiveness on high-dimensional multi-agent nonlinear control problems with state and control dimensions up to 1200 and 400, respectively.
Reinforcement Learning (RL) has been shown to be effective in many scenarios. However, it typically requires the exploration of a sufficiently large number of state-action pairs, some of which may be unsafe. Consequently, its application to safety-critical systems remains a challenge. An increasingly common approach to address safety involves the addition of a safety layer that projects the RL actions onto a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the safety layer to improve the learning performance. In this letter, we frame safety as a differentiable robust-control-barrier-function layer in a model-based RL framework. Moreover, we also propose an approach to modularly learn the underlying reward-driven task, independent of safety constraints. We demonstrate that this approach both ensures safety and effectively guides exploration during training in a range of experiments, including zero-shot transfer when the reward is learned in a constraint-agnostic fashion.
In this paper, the issue of model uncertainty in safety-critical control is addressed with a data-driven approach. For this purpose, we utilize the structure of an input-ouput linearization controller based on a nominal model along with a Control Barrier Function and Control Lyapunov Function based Quadratic Program (CBF-CLF-QP). Specifically, we propose a novel reinforcement learning framework which learns the model uncertainty present in the CBF and CLF constraints, as well as other control-affine dynamic constraints in the quadratic program. The trained policy is combined with the nominal model-based CBF-CLF-QP, resulting in the Reinforcement Learning-based CBF-CLF-QP (RL-CBF-CLF-QP), which addresses the problem of model uncertainty in the safety constraints. The performance of the proposed method is validated by testing it on an underactuated nonlinear bipedal robot walking on randomly spaced stepping stones with one step preview, obtaining stable and safe walking under model uncertainty.
Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs). We consider the setting of a known nonlinear control affine dynamical system and assume that we have access to safe trajectories generated by an expert — a practical example of such a setting would be a kinematic model of a self-driving vehicle with safe trajectories (e.g., trajectories that avoid collisions with obstacles in the environment) generated by a human driver. We then propose and analyze an optimization based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz smoothness assumptions on the underlying dynamical system. A strength of our approach is that it is agnostic to the parameterization used to represent the CBF, assuming only that the Lipschitz constant of such functions can be efficiently bounded. Furthermore, if the CBF parameterization is convex, then under mild assumptions, so is our learning process. We end with extensive numerical evaluations of our results on both planar and realistic examples, using both random feature and deep neural network parameterizations of the CBF. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.
Safe and efficient shape-aware navigation in heterogeneous crowds and robot fleets remains challenging. Traditional approaches often assume homogeneous robots, sparse workspaces, simplified geometry, offline computation, or handcrafted parameters to make the problem tractable, which limits their deployment in dense crowd scenarios. Toward this end, we propose Shape-Aware Reinforcement Learned Model Predictive Control (SRL-MPC), a method for safe, efficient, and adaptive navigation in crowds with heterogeneous shapes without geometry simplification. To encode shape-aware safety, we formulate high-order control barrier function (HOCBF) constraints from geometric separation features (GSFs) based on support function transformation. A reinforcement learning (RL) framework then learns a neural policy that reads GSFs and outputs real-time MPC parameter updates, enabling the MPC solver to adapt to neighboring crowd geometries. The key advantage of SRL-MPC is that it preserves the safety structure and generalizability of MPC while integrating the adaptability and intelligence of RL. Experiments in randomized crowd scenarios with arbitrary shaped robot fleets demonstrate the effectiveness, scalability, and robustness of SRL-MPC. The results show that SRL-MPC substantially outperforms representative baselines in safety and adaptability. Project website: https://hanruihua.github.io/srl_mpc_project/
Reduced-order models based on Cosserat-rod theory are now well established, and modeling theory is no longer the primary bottleneck in soft-robot control. Their implementations, however, do not support the differentiable, GPU-parallel, and control-oriented workflows that underpin advanced rigid-robotics applications. Here, we fill this gap with SoRoMoX (Soft Robot Models in JAX), a fully numerical, JIT-compilable Python/JAX framework. SoRoMoX implements articulated, Piecewise Constant Strain, and Variable Strain models through a unified, control-ready interface that provides inertia matrices, gravitational and elastic forces, Jacobians, and their derivatives. To our knowledge, it is the first rod/strain-based soft-robot modeling framework that runs directly on GPUs and is end-to-end differentiable with respect to states, inputs, and parameters. Sequential CPU rollouts are up to 18.1x faster than state-of-the-art alternatives, while GPU-parallel rollouts increase throughput by up to 234.6x. This performance enables workflows that were previously impractical or impossible: static-equilibrium system identification with 66% lower marker RMSE; residual-force learning with a further 64% reduction; computed-torque tracking with RMSE reduced by a factor of approximately 500 relative to model-free PD; control-gain optimization with up to 62% lower loss than untuned gains; safety-constrained control using high-order control barrier functions to keep the peak contact force within a prescribed 5 N bound, compared with 33.5 N without the safety constraint; and reinforcement-learning policy training up to 7x faster than a CPU PyElastica discrete-rod baseline through massively parallel rollouts.
Safe actor-critic control often treats barrier filtering, uncertainty estimation, and experience replay as separate modules, even though each changes the data used for learning and control. We develop an integrated architecture in which the uncertainty estimate updates the obstacle geometry used by a control barrier function, filter interventions and estimation residuals determine replay priority, and the critic learns from the executed rather than nominal action. We instantiate the architecture on a two-dimensional robot-navigation task with corrupted obstacle measurements and compare six component-matched configurations under common training budgets, random seeds, sensor streams, exploration, and disturbances. Evaluation includes a moderate post-training test, an eleven-level perception-noise sweep, and an exploratory extreme-stress test at multiplier $6.0$. In the extreme test, the integrated configuration recorded no contacts and reached the goal in all five evaluation seeds. Its mean cost was $7.63\pm0.44$ and its obstacle-belief root-mean-square error was $3.52\pm0.55$ cm. The uncertainty-estimation ablation also recorded no contacts but reached the goal in four of five seeds, with mean cost $8.96\pm2.08$ and belief error $11.08\pm1.23$ cm. A finite-training bound clarifies replay exposure, and a robust barrier condition states the required estimation-error and feasibility assumptions. The results support coupling estimation, safety filtering, and replay on this benchmark; broader safety and convergence claims require further study.
Reinforcement Learning (RL) has been shown to be effective in many scenarios. However, it typically requires the exploration of a sufficiently large number of state-action pairs, some of which may be unsafe. Consequently, its application to safety-critical systems remains a challenge. An increasingly common approach to address safety involves the addition of a safety layer that projects the RL actions onto a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the safety layer to improve the learning performance. In this letter, we frame safety as a differentiable robust-control-barrier-function layer in a model-based RL framework. Moreover, we also propose an approach to modularly learn the underlying reward-driven task, independent of safety constraints. We demonstrate that this approach both ensures safety and effectively guides exploration during training in a range of experiments, including zero-shot transfer when the reward is learned in a constraint-agnostic fashion.
Mission-critical intelligent systems often operate under time-varying limitations that reduce control authority and change the admissible safe operating envelope. In such settings, a safety certificate learned under nominal conditions may become invalid as system capability changes. To address this challenge, this paper proposes a degradation-aware, data-driven safety-filtering framework that learns a safe set from data, updates it online, and enforces the resulting learned barrier through a time-varying control barrier function (CBF). A nominal safe envelope is first learned from operational data using a radial basis function (RBF)-kernel support vector machine (SVM), whose decision function serves as the initial CBF candidate. To capture capability-induced safe-set contraction, a continuous-time decremental SVM update law is developed so that selected support-vector coefficients are reduced according to a degradation signal. A homotopy-smoothed SVM-CBF is then introduced to avoid discontinuous changes in the learned barrier during active-set transitions. The resulting time-varying learned barrier is enforced using a quadratic-program-based safety filter under degraded input constraints. Forward invariance of the learned time-varying safe set and recursive feasibility of the safety filter are established. Simulation results on a vertical takeoff and landing (VTOL) model show that the proposed method maintains safety under reduced control authority and avoids abrupt barrier-switching effects during safe-set contraction.
Control invariance validates that dynamical systems have a control input that preserves a given property at all times. This paper introduces a set of sound axioms and proof rules in differential dynamic logic (dL) that enable verification of control invariance. First, the scalar and vector comparison principles, relating a system of differential equations to a comparison system such that invariance properties can be established more easily, are axiomatized in dL. This axiomatization primarily utilizes differential ghosts, which are proof-theoretic generalizations of comparison systems. Next, with the comparison principles serving as the basis, comparison invariants are introduced, and sound axioms and proof rules are derived. Comparison invariants reduce the question of control invariance to a functional inequality on its Lie derivative for a suitable class of functions, moreover, the right choice of function can result in decidable arithmetic. Furthermore, the perennially popular control barrier functions (CBFs) used in safety-critical control are shown to be a special instance of comparison invariants. This yields an axiomatization of CBFs that leads to a dedicated set of proof rules. The rules allow for the verification of CBFs, which are traditionally used for synthesizing safe controllers without verification. Lastly, comparison invariants are shown to unify several other safety verification techniques, including Darboux invariants and differential invariants, further cementing their versatility.
Multi-drone payload transportation has emerged as a promising research paradigm with potential applications in construction, logistics, and disaster response. However, the complex coupled dynamics among drones, cables, and payloads pose significant challenges, and existing approaches remain limited in safety and scalability, particularly in dynamic and unstructured environments. In this work, we propose a learning-based framework for safe and scalable multi-drone cooperative payload transport. We introduce a minimal 2D abstraction that preserves the task-relevant drone-payload coupling required for coordination and safety, while remaining computationally efficient for large-scale learning. Using domain randomization over team size and physical parameters, we train a fully distributed policy via Discrete Graph Control Barrier Function Proximal Policy Optimization (DGPPO), enabling robust zero-shot sim-to-real transfer without fine-tuning. Extensive real-world evaluations demonstrate that a single learned policy generalizes across varying team sizes and task scenarios. Furthermore, multi-group hardware experiments show that the same policy can safely operate in dynamic environments, where other drone teams act as moving obstacles. These results indicate that the proposed framework enables efficient, safe, and scalable multi-drone payload transportation with strong generalization to complex real-world conditions.
This paper studies energy-efficient operation of autonomous vehicles (AVs) in dynamic environments with moving obstacles and while communicating over mmWave channels. The obstacles induce severe attenuation of the mmWave channel resulting in a highly dynamic communication environment. In this setting, we consider the problem of jointly optimizing motion and communication energy for an AV that safely navigates among dynamic obstacles toward a designated destination while ensuring timely transmission of onboard sensing or telemetry data over mmWave channels. We then seek a real-time methodology to compute energy-efficient trajectories in a setting where dynamic obstacles induce both safety constraints and time-varying mmWave blockage, leading to tightly coupled motion-communication trade-offs. We propose a nonlinear model predictive control (NMPC) framework that enables anticipative communication and motion decision-making and energy co-optimization, augmented with a control barrier function (CBF) to ensure safety. Extensive simulation results demonstrate the effectiveness of our approach, reducing total energy consumption by up to 37.3% compared to baseline strategies. Overall, our results demonstrate that the proposed NMPC-based framework significantly enhances energy efficiency and performance of AVs under dynamic, blockage-sensitive mmWave communication constraints.
This paper presents a safety-critical bilateral teleoperation framework for omnidirectional aerial manipulators that integrates visual and force-sensorless haptic wrench feedback. Unlike existing approaches that either rely on onboard force/torque sensors or use model-dependent wrench estimates, which may become unreliable under model uncertainties or induce unintended feedback during free-flight, our method implements a hierarchical safety filter based on control barrier functions to avoid such limitations. The safety filter, being the key contribution, explicitly accounts for tracking errors arising from physical interaction between the aerial manipulator and its surroundings while enforcing thrust limits, a factor overlooked despite its critical importance for flight safety. This safety filter adjusts the command from the operator to ensure safe and stable aerial manipulation and avoid motor saturation. The adjustment made by the filter is mapped to haptic feedback, which is intuitive to the operator and conveys information on physical interaction and impending motor saturation. By actual experiments with a hexarotor-based omnidirectional aerial manipulator, we demonstrate that the proposed method avoids haptic feedback during free-flight, provides directionally consistent feedback under physical interaction, and can be operated for diverse manipulative tasks. Moreover, an ablation study further shows that the saturation filter improves interaction stability by explicitly preventing motor saturation and informing the operator of corrective actions.
Safe model-based reinforcement learning (RL) often bridges control-theoretic analysis and RL for robots to safely explore (partially) unknown system dynamics while deriving control actions for task efficiency. The control performance and safety assurance typically rely on prior knowledge of partially modeled nominal system dynamics and the data-driven models that compensate for residual model uncertainties. However, existing methods often overlook the structure of residual model uncertainties (e.g., components affine in control), which could lead to overly conservative robot behaviors or invalid safety guarantees under the safe learning-based controllers. This paper proposes a safe reinforcement learning framework that learns control-affine dynamics with a certifiable data-driven safe policy using control barrier functions (CBF). Specifically, we first use Control-Affine Random Fourier Features (ARFF) to model robot dynamics in a control-affine form, which offers computational efficiency that scales with dataset size and reduces potential model bias for model-based reinforcement learning. Then, a model-free, efficient uncertainty quantification method using adaptive conformal prediction (ACP) is applied to quantify the uncertainty in the safety constraint arising from the learned control-affine dynamics. This allows for data-driven safety assurance amenable to principled and efficient controller synthesis with CBF. Simulation results on the cartpole and the 3D quadrotor platforms demonstrate the effectiveness of the proposed framework.
Reinforcement Learning (RL) has demonstrated remarkable capabilities for solving complex robotic control problems, but its lack of safety guarantees severely limits deployment on hardware. In particular, as legged robots and manipulators often operate near safety-critical boundaries, out-of-distribution states can lead to failure upon deployment. To address this, we introduce Acc-CBF-QP, an acceleration-based Quadratic Program (QP) safety filter using Control Barrier Functions (CBFs) that constrains any RL policy onto a safe set at runtime without modifying training. The method applies to unconstrained and Safe-RL policies, and enforces joint position, velocity, torque, and collision constraints within a unified optimization framework. A key contribution is the formulation of RL+QP tasks that regulate deviation from the RL command when constraints would otherwise be violated. We introduce a TorqueTask, minimizing torque deviation, and a Forward Dynamics Task, minimizing induced acceleration deviation, thus providing principled control over safety-performance trade-offs. Experiments on a 7-DoF Kinova Gen3 manipulator and a 19-DoF Unitree H1 humanoid, both in simulation and on hardware, highlight substantial reductions in constraint violations. On the real H1 hardware, a Safe-RL policy alone yielded 10.04 violations/s, which were reduced by 92% to 0.80 violations/s when augmented with Acc-CBF-QP. On the Kinova Gen3, Acc-CBF-QP fully eliminated violations. Nominal task performance of the RL objective is preserved in violation-free regimes. Under aggressive velocity commands on H1, Acc-CBF-QP improves execution by preventing constraint-induced shutdowns, yielding longer survival times. The full pipeline is open-source.
Redundant robotic manipulators operating in constrained and human-interactive environments require accurate task-space tracking together with rigorous safety guarantees under dynamic uncertainties. Classical operational space computed torque controller (OSCTC) relies on accurate dynamic models and degrades in the presence of disturbances. In contrast, the data-driven paradigm of residual learning approximates disturbances as functions learned from full-state measurements, which are often noisy in practice, lack rigorous theoretical guarantees, and introduce additional design complexity. This paper proposes a robust OSCTC framework that integrates an extended state observer (ESO) with conformal prediction to combine model-based robustness and data-driven adaptability. The ESO estimates lumped disturbances directly in operational space without requiring full-state measurements as in residual learning, and a robust control barrier function (CBF) is constructed to enforce safety under uncertainty. However, robust CBFs require a known disturbance-variation bound to guarantee absolute safety, which often leads to conservatism in practice. To address this limitation, we further employ a sliding-window conformal prediction mechanism to estimate the bound online in a distribution-free manner, thereby achieving practical probabilistic safety guarantees. Experiments on a 7-DoF Franka Research 3 manipulator demonstrate millimeter-level tracking accuracy and real-time safe control at 1~kHz under various disturbances.
Cooperative aerial transport requires controllers that respect nonlinear manifold geometry, operate without centralized coordination, and respect operational safety constraints. To address these demands, we present GPAC, a four-layer hierarchical architecture that enables $N$ quadrotors to transport a cable-suspended payload without a central coordinator or by exchanging cable states or adaptive parameters. The key insight is implicit coordination: each quadrotor independently estimates its effective load share from local cable measurements, so combined forces converge to the correct total, even without knowledge of $N$ or the payload mass; the payload position is reconstructed locally from each agent's own cable geometry, and the only inter-agent communication is a low-rate neighbor-position broadcast for collision avoidance. GPAC operates directly on the full nonlinear configuration manifold and integrates geometric position and attitude control, anti-swing regulation, an extended-state observer for wind rejection, concurrent learning-based mass estimation without persistent excitation, and a priority-ordered control barrier function (CBF)-inspired safety filter that reduces operational risk, with input-to-state safety (ISSf) margins that hold exactly under single-constraint activation. A compatibility result shows that the filter's force modifications keep the desired attitude within the almost-global stability region of the $\mathrm{SO}(3)$ attitude controller. Finally, high-fidelity simulation with flexible cables, onboard sensor fusion, and wind turbulence -- with all control and estimation loops closed through the estimator -- yields a mean payload-tracking RMSE of 33.8 cm (2.8\% coefficient of variation over 13 seeds) at a low per-agent computational cost.
Cooperative transport and manipulation of heavy or bulky payloads by multiple manipulators requires coordinated formation tracking, while simultaneously enforcing strict safety constraints in varying environments with limited communication and real-time computation budgets. This paper presents a distributed control framework that achieves consensus coordination with safety guarantees via hierarchical event-triggered control barrier functions (CBFs). We first develop a consensus-based protocol that relies solely on local neighbor information to enforce both translational and rotational consistency in task space. Building on this coordination layer, we propose a three-level hierarchical event-triggered safety architecture with CBFs, which is integrated with a risk-aware leader selection and smooth switching strategy to reduce online computation. The proposed approach is validated through real-world hardware experiments using two Franka manipulators operating with static obstacles, as well as comprehensive simulations demonstrating scalable multi-arm cooperation with dynamic obstacles. Results demonstrate higher precision cooperation under strict safety constraints, achieving substantially reduced computational cost and communication frequency compared to baseline methods.
Current Vision-Language-Action (VLA) models rely primarily on RGB perception, preventing them from capturing modalities such as thermal signals that are imperceptible to conventional visual sensors. Moreover, end-to-end generative policies lack explicit safety constraints, making them fragile when encountering obstacles and novel scenarios outside the training distribution. To address these limitations, we propose Safe-Night VLA, a multimodal manipulation framework that enables robots to see the unseen while enforcing rigorous safety constraints for thermal-aware manipulation in unstructured environments. Specifically, Safe-Night VLA integrates long-wave infrared thermal perception into a pre-trained vision-language backbone, enabling semantic reasoning grounded in thermodynamic properties. To ensure safe execution under out-of-distribution conditions, we incorporate a safety filter via control barrier functions, which provide deterministic workspace constraint enforcement during policy execution. We validate our framework through real-world experiments on a Franka manipulator, introducing a novel evaluation paradigm featuring temperature-conditioned manipulation, subsurface target localization, and reflection disambiguation, while maintaining constrained execution at inference time. Results demonstrate that Safe-Night VLA outperforms RGB-only baselines and provide empirical evidence that foundation models can effectively leverage non-visible physical modalities for robust manipulation.
Traditional safety-critical control methods, such as control barrier functions, suffer from semantic blindness, exhibiting the same behavior around obstacles regardless of contextual significance. This limitation leads to the uniform treatment of all obstacles, despite their differing semantic meanings. We present Safe-SAGE (Social-Semantic Adaptive Guidance for Safe Engagement), a unified framework that bridges the gap between high-level semantic understanding and low-level safety-critical control through a Poisson safety function (PSF) modulated using a Laplace guidance field. Our approach perceives the environment by fusing multi-sensor point clouds with vision-based instance segmentation and persistent object tracking to maintain up-to-date semantics beyond the camera's field of view. A multi-layer safety filter is then used to modulate system inputs to achieve safe navigation using this semantic understanding of the environment. This safety filter consists of both a model predictive control layer and a control barrier function layer. Both layers utilize the PSF and flux modulation of the guidance field to introduce varying levels of conservatism and multi-agent passing norms for different obstacles in the environment. Our framework enables legged robots to safely navigate semantically rich, dynamic environments with context-dependent safety margins.
Vision-Language-Action (VLA) models have demonstrated remarkable capabilities in generalizing across diverse robotic manipulation tasks. However, deploying these models in unstructured environments remains challenging due to the critical need for simultaneous task compliance and safety assurance, particularly in preventing potential collisions during physical interactions. In this work, we introduce a Vision-Language-Safe Action (VLSA) architecture, named AEGIS, which contains a plug-and-play safety constraint (SC) layer formulated via control barrier functions. AEGIS integrates directly with existing VLA models to improve safety with theoretical guarantees, while maintaining their original instruction-following performance. To evaluate the efficacy of our architecture, we construct a comprehensive safety-critical benchmark SafeLIBERO, spanning distinct manipulation scenarios characterized by varying degrees of spatial complexity and obstacle intervention. Extensive experiments demonstrate the superiority of our method over state-of-the-art baselines. Notably, AEGIS achieves over 50% improvement in obstacle avoidance rate while substantially increasing the task success rate by nearly 10%. All benchmark datasets, code, and supplementary materials are publicly available at https://vlsa-aegis.github.io/.
Connectivity is crucial in many multi-robot applications, yet balancing connectivity maintenance and fleet traversability in obstacle-rich environments remains challenging. Reactive controllers based on control barrier functions can preserve connectivity when it is initially satisfied, but often struggle with deadlocks in cluttered environments. We propose a real-time Bézier-based constrained motion planning algorithm, namely MPC--CLF--CBF, that produces trajectories and control inputs concurrently, subject to high-order control barrier function and control Lyapunov function constraints. Our motion planner supports connectivity-aware navigation in cluttered workspaces and recovers connectivity from initially disconnected configurations and after temporary obstacle-induced separation; it also provides analytic continuous-time derivatives, facilitating its application to agile differentially flat systems such as quadrotors. In simulations with $4$--$12$ robots, it maintains $95.8$--$100\%$ graph-connected time at $20\%$ obstacle density, compared with $48.9$--$61.3\%$ for MPC--CBF, with no observed collisions. We further validate the planner in a physical experiment with $8$ Crazyflie nano-quadrotors.
Autonomous 3D active mapping requires a space robot to choose where to sense while building the geometry needed for navigation. Learned occupancy completion extends spatial context beyond the current field of view, but one predicted map often serves two planning roles: it scores expected surface gain and constrains collision-free motion. Unsupported occupancy can therefore distort both where the robot looks and where it believes it can travel. We study this coupled interface in a controlled closed-loop benchmark by holding the active-mapping system fixed and varying only its planner-facing occupancy across observation-only, learned, oracle-corrected, and ground-truth conditions. Improving occupancy accuracy does not monotonically improve closed-loop coverage: across 25 starts, planning with ground-truth occupancy reaches 70% of the learned baseline's final coverage 12.7 steps earlier on average, while increasing final coverage by only 0.031. Guided by this diagnosis, we introduce an observation-gated filter that retains completion in insufficiently observed regions and suppresses predictions only after repeated frustum exposure without nearby RGB-D support. The filter improves both targeted failure-prone starts without retraining or ground truth. These results motivate online revision of planner-facing geometry during autonomous intervals between communication windows. The current study assumes benchmark RGB-D observations and sufficiently accurate pose estimates; planetary sensing conditions and accumulated localization drift remain to be evaluated.
Robotic construction offers the potential to use materials more efficiently and create complex geometries, but current methods rely on rigid, high-precision plans that cannot accommodate the tolerances, inaccuracies, and unexpected changes inherent in physical fabrication. In this work, we introduce a reinforcement learning approach that forgoes predefined plans entirely, instead generating construction sequences adaptively as the structure is built. Our method operates on graph-structured state representations and a mixed (parameterized) action space, requiring both discrete block selection and continuous placement parameters. Because the stability simulation of a structure is computationally heavy, we develop an efficient exploration strategy by incorporating unilateral edges into graph neural networks, extending soft actor-critic (SAC) to this hybrid setting. We evaluate our algorithm, HSAC, against the prior method hybrid-PPO (HPPO), demonstrating significantly higher asymptotic performance and good sample efficiency. We also demonstrate HSAC's robustness to hyperparameter choices and its exploration capability, handling up to 10 discrete actions without performance degradation. Finally, we validate our approach on a physical two-robot setup, successfully building a spanning arch with 3D-printed blocks in closed-loop execution, confirming that policies trained in simulation transfer to real hardware.
Surface coverage with task-redundant manipulators is challenging because each surface point may admit multiple inverse kinematics (IK) solutions, and configuration choices strongly affect motion quality. This paper extends the classical Spanning Tree Coverage (STC) method to redundant manipulators through offline and online Joint Spanning Tree Coverage (JSTC) algorithms. Offline JSTC samples multiple Inverse Kinematics (IK) solutions per grid cell and formulates the problem as a Generalized Minimum Spanning Tree (GMST), selecting one configuration per cell and tracing the resulting tree to obtain a non-revisiting coverage path. Online JSTC incrementally expands and backtracks a spanning tree with feasibility and cost evaluation while handling dynamic grid updates. Simulation results show that offline JSTC reduces computation time, reconfigurations, and joint motion compared to other methods, while online JSTC achieves fast per-step planning in dynamic scenarios.
Anticipating whether a person will interact from one's own perspective is a highly intuitive task for humans, that relies on a combination of cues. We investigate how humans perform at predicting a person's intention to interact from a service robot's point of view, using pose-only or full video input, then benchmark different lightweight pose-based models and state-of-the-art vision-language models. We conducted our benchmark on the HUI360 dataset on a fixed pilot subset of 100 test tracks (25 positive, 75 negative). We found that with pose-only input, human annotators outperform lightweight trained pose models but not by large margins (+0.08 in F1-Score). But when given full egocentric video with a target bounding box, human annotators perform substantially better and largely outperform the Vision-Language Models (+0.2 in F1-Score). We also compared VLMs of different size and under different input conditions, and found that the best results do not correlate with model size. Our result confirms that predicting interactions is a challenging task for social robots and that reasoning-capable models are necessary but their actual reasoning capabilities alone do not suffice to match the social intuition of humans.
SLAM systems based on 3D Gaussian Splatting (3DGS) have recently demonstrated promising reconstruction accuracy for dense 3D scene representations. However, current 3DGS systems struggle to meet the strict demands of real-world deployments due to severe limitations in operational performance and map adaptability. To this end, we propose LightSplat, a hybrid-representation RGB-D SLAM framework. It synergizes local sparse features for robust and fast tracking with a dual-thread backend that progressively constructs dense Gaussian submaps. Crucially, we enable online loop closure through feature-accelerated 3DGS registration, refining overall map consistency through pose graph optimization. Ultimately, LightSplat achieves the online reconstruction of high-fidelity Gaussian map. Extensive experiments on multiple datasets and real-world robotic platform demonstrate that our method achieves near state-of-the-art reconstruction quality and the capability to accommodate practical camera motions, maintaining an average framerate of 8 FPS. Overall, LightSplat provides an efficient and robust foundation for deploying high-fidelity 3DGS in real-world environments.
Estimating the 6D pose of textureless objects without prior CAD models remains a critical challenge due to the lack of appearance features. While recent generalizable approaches alleviate the dependence on object-specific models, their performance on low-texture objects is often limited by insufficient geometric constraints in the underlying representations. In this work, we propose PG-Pose, a geometry-aware framework combining Planar-based Gaussian Splatting (PGS) reconstruction and Geometry-driven pose optimization. In the offline representation extraction stage, three distinct representations of the object are extracted from multi-view reference RGB images with known poses. PG-Pose reconstructs a 3D Gaussian representation and renders high-fidelity depth maps to generate 3D point clouds through back projection. In the online pose inference stage, the initial pose of the input image is estimated by 2D-3D correspondence matching between the input image and the reconstructed 3D point clouds, followed by a PGS-Refiner for iterative pose optimization. Evaluations on the OnePose-LowTexture datasets, PG-Pose achieves an average accuracy of 94.2% ADD(S)@0.1d, with a 2.1% improvement average accuracy compared with the state-of-the-art (SOTA) GS-based approach. To further demonstrate the effectiveness of PG-Pose for industrial robots in grasping tasks, we deploy it on a dual-arm industrial robot and successfully realize the grasping task on an unseen object.
Active mapping requires a robot to select camera viewpoints that efficiently reconstruct an unknown 3D scene. To reason about unobserved regions, recent systems use pretrained occupancy networks as world models that complete missing geometry. The predicted structure contributes to expected coverage gain and constrains feasible robot motion. Consequently, occupancy errors can change both what the robot chooses to explore and where it is able to move. We diagnose these effects by holding the planner fixed and varying only the occupancy representation provided to it. We consider planning without completion, with learned occupancy, with false positives removed by a ground truth oracle, with false negatives restored by an oracle, and with ground truth occupancy. Our experiments show that correcting false positives or false negatives alone does not consistently improve final coverage. This finding reveals a gap between occupancy accuracy and downstream planning performance. Ground truth occupancy provides a much larger improvement in coverage efficiency than in endpoint coverage, suggesting that planning and reachability remain important bottlenecks even when the geometric world model is accurate. Based on these findings, we introduce a dynamic filtering strategy that preserves predictions in unexplored space while suppressing repeatedly unsupported occupancy using online observations. Preliminary examples show that this strategy can redirect viewpoint selection toward reachable surfaces that would otherwise remain unobserved.
Achieving robust SLAM in large-scale underground coal mines with complex structures and severe degeneracies remains highly challenging. Dense smoke and dust cause substantial loss of visual information and degrade LiDAR point-cloud features, while long, self-similar corridors induce geometric degeneration, leading to pronounced odometry drift. To address these issues, we propose FIRE-LIVWO: Failure-Immune mmWave Radar-Enhanced LiDAR-Inertial-Visual-Wheel Odometry, a tightly coupled multi-modal odometry framework based on an iterated error-state Kalman filter (IESKF). The framework fuses 4D mmWave radar, LiDAR, and visual features within a unified VoxelMap and jointly constructs LiDAR-radar point-to-plane residuals and sparse visual photometric residuals. In smoke-filled environments, we exploit the strong penetration of 4D mmWave radar and introduce pointwise Doppler velocity constraints to preserve state observability. In geometrically degenerate corridors, we tightly couple wheel odometry using non-holonomic constraints (NHC) and online lever-arm compensation to reduce drift. Our central contribution is a degeneration detection and adaptive fusion model switching strategy grounded in geometric and visual observability analysis, which quantifies observability online and dynamically adjusts modality weights. Real-world experiments in underground coal mines demonstrate that FIRE-LIVWO accurately identifies failure boundaries, enabling reliable modality switching under extreme conditions. Compared with baselines, it achieves superior accuracy and robustness (average localization error of 5.677m). We open source our code on Github to benefit the robotics community.
Quadruped robots have demonstrated impressive agility in parkour locomotion across complex terrains. However, most systems still rely on human intervention for high-level planning, and autonomous parkour navigation remains underexplored. The key challenges include fine-grained velocity regulation, long-horizon anticipatory behaviors, and tight coupling between perception and embodied execution. To address these challenges, we propose a Multimodal Diffusion Policy (MulDP) that integrates visual perception with robot proprioception and goal information to generate temporally coherent and anticipatory navigation velocity commands, tightly coupling perception with embodied control to enable robust autonomous navigation. To support the training of MulDP, we construct the first Quadruped Parkour Navigation Dataset (QPND), a multimodal dataset that encompasses diverse navigation behaviors and complex terrains. Extensive simulation and real-world experiments demonstrate that MulDP enables robust long-horizon autonomous navigation and effective traversal across complex terrains.
Action-conditioned JEPA world models enable planning toward visually specified goals without reconstructing future pixels, yet latent prediction alone does not explicitly encourage the learned representations to retain information relevant to robotic control. We introduce an end-to-end JEPA world model that augments latent prediction with inverse dynamics (IDM) and state alignment (SA). While inverse dynamics discourages latent collapse and makes latent transitions informative of the actions that produced them, state alignment grounds consecutive representations in their associated physical configuration and motion. Across four benchmark tasks, our model attains the highest success rates on TwoRoom (100%), PushT (98%), and OGBench-Cube (87%), while performing comparably to LeWorldModel on Reacher. Our ablation further shows that adding state alignment consistently improves planning success over IDM alone across all four tasks. Although LeWorldModel, our primary baseline, attains higher average straightening on OGBench-Cube, transition-subspace analysis shows that its transition energy is concentrated in a substantially lower-dimensional subspace. Our state-aligned model exhibits a higher effective transition dimension than LeWorldModel and improves planning over IDM alone, supporting state alignment as an effective complement to inverse dynamics for robotic planning.
This study proposes a novel Model Predictive Path Integral (MPPI)-based task-space control framework. The proposed framework explicitly solves rigid-body dynamics within a real-time MPC formulation and enforces safety constraints, enabling accurate motion and force control that yields compliant behaviors for safe and effective physical interaction of robotic manipulators in unstructured environments. By leveraging MPPI, the proposed framework efficiently handles nonlinear dynamics that are difficult to solve with conventional MPC approaches in real-time. Furthermore, we develop a torque-sampling-based control architecture that enables efficient exploitation of GPU-based parallelization, resulting in effective compliant and force-aware behaviors. As a result, the proposed framework achieves a solver update rate of over 166 Hz with a 0.18 s prediction horizon, and its performance is validated through real-world experiments on a 7-DoF manipulator.
Robotic throwing enables fast object transport and extends a robot's reachable workspace beyond traditional pick-and-place. While prehensile (grasp-based) throwing works well for graspable items, non-prehensile (grasp-free) throwing is better suited for large, heavy, and/or deformable objects. Existing approaches rely on model-based optimization with simplified contact models (e.g., dynamic grasping) and low-dimensional trajectory parameterizations, which limit solution quality and reachable workspace. We propose a reinforcement learning approach that additionally leverages sliding and rolling contact modes and directly optimizes joint-space trajectories without analytical contact models or custom parameterizations. The Markov Decision Process (MDP) is formulated as a dynamical system that evolves the robot's joint state conditioned on the throwing target, object model, and initial configuration. Joint-jerk trajectories are planned offline at a low control rate and upsampled into smooth, high-rate velocity commands for deployment. For sim-to-real transfer, we minimize the robot-dynamics gap through minimum-jerk system identification and train uncertainty-aware policies to mitigate object-modeling errors, particularly sensitivity to dynamic friction. In simulation, the policy achieves 99% success across thousands of configurations and generalizes to unseen objects. Sensitivity analysis shows robustness to mass uncertainty but high sensitivity to dynamic friction, consistent with the sliding-based release mechanism. Deployed zero-shot on a UR5e operating near its physical limits (5 m/s end-effector velocity), our method throws diverse objects including heavy (790 g) and large (20x20x28 cm) items to targets up to 350 cm distance or 180 cm elevation, achieving a 97% real-world success rate.
Vision-Language-Action (VLA) models, built upon Vision-Language Models (VLMs), have significantly enhanced robotic capabilities by leveraging internet-scale knowledge and multimodal reasoning. However, the intensive computational overhead of VLAs constrains on-device deployment, hindering real-time responses to environmental changes. While various acceleration techniques have been proposed, they often rely on fine-tuning or access to training datasets, which are frequently unavailable due to privacy and proprietary concerns. Moreover, although flow-matching-based VLAs have emerged as efficient alternatives to standard diffusion models, current acceleration efforts largely target VLM inference costs, failing to address the iterative ODE solving process inherent in flow matching inference. To address these limitations, we propose AdaVLA, an online, training-free adaptive framework for fast yet accurate flow-matching-based Vision-Language-Action models. We introduce a novel metric derived from the flow matching trajectory curvature to quantify action generation confidence during inference. This metric enables the dynamic reduction of inference steps and the adaptive adjustment of MLP pruning ratios through an efficiently computed importance evaluation, requiring no access to training data. Experimental results on the LIBERO benchmark using a Jetson AGX Orin device demonstrate that our method achieves $1.87\times$ and $2.24\times$ speedups for $π_{0.5}$ and X-VLA, respectively, with negligible degradation in success rates. Furthermore, we validate the robustness of our approach on real-world robotic tasks using SmolVLA.
Bin-picking is a cornerstone of modern manufacturing, yet achieving complete bin clearance without manual intervention remains a critical challenge. While model-based methods provide high precision, they frequently suffer from deadlocks when predefined grasps are occluded or perception fails. Labor-intensive fine-tuning of grasp points is commonly required to reach a satisfactory performance for new parts. Model-free algorithms offer a more flexible alternative with "out-of-the-box" versatility but lack the reliability and repeatability required for production. Unlike existing work, which treats the two techniques in isolation, we propose a fourtiered hierarchical hybrid approach to combine the best of both worlds. A model-based pipeline serves as a robust backbone, while a model-free "exploration agent" resolves deadlock situations and discovers new grasp points. This is supported by an online self-learning mechanism that uses gripper-stroke feedback and Wilson score intervals to autonomously rank grasp candidates, reducing manual commissioning effort. Validation on three automotive parts demonstrates that our method significantly outperforms a model-free baseline in grasp success rate while improving the bin clearance rate of the model-based baseline from 50.9% to 100% across all experiments. This transition to full bin clearance marks a significant step towards truly autonomous, intervention-free industrial operation.
We study the problem of decentralized, self-organized task sharing for a swarm of heterogeneous robots that collaborate in transportation or other objectives that require coordinated motion planning. To this end, we present theoretical and practical results for the simple but effective mechanism of \emph{bucket brigades} for load balancing, in which a team of heterogenous robots share a spatial task in a confined, one-dimensional space, while only being able to sense collisions with neighbors or walls. The goal is to optimize throughput of the overall system, without central control or information, aiming at an interval partition proportional to robot velocities. We address possible chaotic system behavior by developing a stabilization mechanism based on simple local aid, a ``token'', that temporarily decelerates robots after an encounter. This purely local change eliminates persistent oscillations, resulting in convergence towards a stable system state. We accelerate system convergence by comparing a single boundary token to ubiquitous two-directional tokens and optimizing the deceleration factor. Event-driven simulations report convergence times and robustness: For a large variety of perturbations (such as robot deletion, position or velocity jittering), the system reliably re-converges. The results suggest a local, practical mechanism for robust load balancing for heterogeneous teams of robots that promises an effective tool as basis for more complex scenarios.
Intent misinterpretation during vehicle interactions causes recurring planning failures. We study a decision layer in which a language-guided intent module reads structured descriptors, computes a smoothed intent-geometry divergence score, and gates the planned maneuver before commitment, upstream of a corridor envelope. On a replayed off-road departure and four crash clips under a frozen, disclosed implementation, gating is the only layer that repairs the plan: on the main case it fires 72 ms after the drift onset but 161 ms before the corridor exit, keeping the trajectory in the corridor in all ten replays. The first calibration draws nine false triggers in 5.9 minutes, each from scoring uncertainty as half a conflict; a preregistered redesign treating uncertainty as abstention cuts this to 0.341 per minute. Two ablations bound the model's contribution: the full score detects fastest on four of five failures under the deployed eligibility, three of five against the unvetoed rule (000871 by one cycle; 000228 by a pre-onset fire on an uncertain stretch that five clips cannot classify as signal or coincidence; dropping the confidence term costs two detections), while on in-domain tracks at equal false positives the geometric rule more than triples its detection. The evidence supports the gating mechanism; the model's demonstrated roles are the fastest detection on these failures and an uncertainty veto on the geometric rule.
Advanced automation is a key technology for enhancing the safety of ground operations amidst the increasing density of commercial air traffic. While motion forecasting is a well-studied task in autonomous driving, its application to airport surface movements remains underexplored. To enable efficient and accurate prediction in this domain, we propose DESCENT, a transformer-based architecture designed to handle heterogeneous dynamics and strict topological constraints. Our approach features a Potential Reachable Set (PRS) context sampling mechanism that adaptively collects airfield environment context across diverse operational phases. Combined with a detection transformer-based decoder, DESCENT generates accurate trajectory forecasts. Extensive evaluations on the Amelia-10 benchmark demonstrate significant performance improvements over state-of-the-art baselines. These gains are especially pronounced in safety-critical scenarios, where our domain-aware sampling provides critical long-horizon context necessary for safe navigation.
Tactile sensing is central to robotic manipulation, among which slip detection stands out as a quintessential and critical task. However, existing slip datasets are predominantly limited to binary classification, lacking fine-grained directional perception. To address this limitation, we propose a visuo-tactile sensor featuring customized uniform RGB illumination, alongside a unified perception framework. At the hardware level, the sensor achieves high-precision, sub-millimeter depth reconstruction. Based on this capability, we collect a multi-task visuo-tactile dataset encompassing 15 objects, synchronously generating depth information for each data sample. Algorithmically, we design a dual-head TimeSformer network to process dynamic spatiotemporal slip. On unseen objects, this network achieves robust accuracies of 95.5% and 91.5% for 3-class contact state prediction and fine-grained 8-class slip direction classification, respectively. Furthermore, static tactile-based object class recognition utilizing a ResNet-50 backbone yields an outstanding accuracy of 98.8% across 15 categories. The proposed hardware-software framework provides high-fidelity feedback and a powerful multi-modal perception baseline for complex robotic manipulation.
Proprioception in musculoskeletal humanoids is typically estimated primarily from muscle sensing, while the role of cutaneous deformation around joints remains insufficiently explored. In biological systems, mechanoreceptors distributed within soft tissue complement muscle feedback and support reliable joint state estimation. This study presents the design of a biomimetic joint-covering skin with a tissue-like layered structure that integrates pressure- and stretch-sensitive elements within the joint-covering tissue. The proposed skin is implemented on the musculoskeletal humanoid Musashi-W, and its independent proprioceptive capability as well as its integration with muscle sensing are evaluated. Experimental results show that the proposed skin alone achieves joint angle estimation with an average error of approximately 3 degrees. Furthermore, integration with muscle sensing improves estimation accuracy. Owing to its joint-covering structure, the skin may mechanically mitigate the influence of external disturbances on the muscles, and the integration of multiple modalities suggests the possibility of contributing to the identification of external stimuli that are difficult to interpret using muscle sensing alone. This work presents a design methodology for biomimetic joint-covering skin and demonstrates that such tissue-structured skin can serve as an effective approach for extending proprioceptive systems in musculoskeletal humanoids.
Multifingered grasping is a crucial robotic skill, but current deep-learning grasp planners often struggle to generalize to new objects because they are trained on limited, object-specific datasets. We introduce a fundamentally different approach, grounded in the observation that the gripper and the object share identical surface geometry at their mutual contact points. We propose GOAG: Generative and Object-Agnostic Grasp Planner for Dexterous Robotic Manipulation, a novel deep generative model that learns a compact latent representation of a specific gripper's contact surface distribution, enabling the efficient sampling of valid grasp configurations without relying on object-specific training data. We show that by introducing object features only at inference time, our model can effectively retrieve admissible contact areas that are compatible with the gripper's capabilities. We validate our approach through extensive experiments on established grasp protocols in both simulated and real-world scenarios, demonstrating its effectiveness with different grippers from the literature. Our method delivers state-of-the-art results on the objects from the MultiDex dataset, achieving an average success rate of 86.93%. It offers significantly faster processing when generating numerous grasps, while matching the performance of leading approaches specifically trained on this dataset. Unlike these methods, our approach does not rely on object-specific training data, highlighting the advantages of object-agnostic learning. It effectively addresses the generalization challenges faced by traditional data-driven grasp planners. Code and videos are available on our project website https://cea-list.github.io/goagweb/ .
Recent studies investigate how to leverage pre-collected datasets to improve the policy performance and sample efficiency of RL. One promising approach to achieve this goal is to employ a two-stage strategy: In the first stage, diverse skills are extracted as a low-level policy from a given dataset, and a high-level policy is trained to solve a specific task in the second stage. Typically, extraction of the low-level policy is performed based on unsupervised learning such as trajectory VAE. However, a limitation of this approach is that the quality of the low-level policy highly depends on the quality of the dataset. To address this issue, we introduce QDOS (Quality-Diversity Offline Skill learning), a unified pipeline for robust offline-to-online learning. Our approach incorporates an Advantage-Weighted Quality-Diversity pretraining objective, which weights the skill extraction and diversity objectives by the estimated advantage of each trajectory segment. This approach allows the model to extract diverse and high-value skills. By providing robust and task-relevant skill representations, QDOS significantly improves the quality of the embedded skill space used by the low-level policy. We further integrate this with a dual dataset reuse strategy, where offline data is used both for skill pretraining and for populating the online replay buffer via pseudo-labeling. Experiments demonstrate that QDOS significantly outperforms strong baselines in structured manipulation tasks and unstructured locomotion tasks, confirming its ability to accelerate exploration and improve final returns in challenging sparse-reward domains.
Subsea Christmas Trees (XTs) are underwater structures that use valves for directing oil flow, needing constant inspection. But not every valve carries the same risk at the same time: a valve with a suspected leak needs to be revisited far more often than one with a clean history, and that risk picture changes during the mission as new leaks are found. To handle this, we present SAGE (Semantic and Adaptive Generative Ergodicity), an ergodic-control architecture that allocates vehicle time in proportion to a live, sensor-derived risk distribution rather than a scripted route. We study a two-XT scenario, with five valves in total, and compare a fixed-loop A* tour against SAGE. Both methods can be tuned to spend similar total time near a high-risk valve, but only ergodic control also checks it more often: in simulation, a dominant-risk valve was revisited every 5.8 s under ergodic control against a fixed 8.1 s for every valve under A*, regardless of risk, so a leak can go unnoticed for barely two-thirds as long. Because the tracked distribution is recomputed rather than planned once, a newly detected leak shifts vehicle behavior on the next control cycle with no explicit re-planning step and no operator in the loop, which a fixed tour cannot do without a discrete re-route. We derive the ergodic control law behind this behavior and report simulation results on the five-valve scenario.
Large language models can turn a natural-language mission into a sequence of robot actions, but they do not have a sense of physics: they cannot judge how long a command should run, or whether it will make the robot drift into an obstacle. We proposed the use of a world model to expand the capabilities of Large Language model-based planners. Our method has three components: a physics-grounded neural world model, a three-phase gradient-based trajectory optimizer, and a Model Predictive Controller (MPC)-style closed-loop replanner with a trust-region guard. The language model decides what to do, and the world model decides how long, whether that means driving eight thrusters through 6 DOF or two differential thrusters through 3 DOF. We evaluate two marine vehicle classes operating near offshore wind infrastructure: a 6-DOF Autonomous Underwater Vehicle (AUV) and a 3-DOF differential-drive Autonomous Surface Vehicle (ASV). In five benchmark missions per platform, both vehicles reach every goal with zero predicted collisions, and both transfer to GazeboSim under ocean current, waves, and thruster dynamics, remaining collision-free and cutting GazeboSim goal-distance error versus the ungrounded baseline by 70-82% (ASV) and roughly 93% (AUV), after a residual fine-tuning pass that separately reduces surrogate rollout Root Mean Square Error (RMSE) by 60% (AUV) and 69% (ASV). For the ASV we further demonstrate a Vision language model (VLM)-assisted semantic-mapping pipeline that extracts obstacles and environmental context from satellite imagery, nautical charts, and forecast Application Programming Interface (API) instead of onboard sensors, reaching 96% navigability accuracy as a drop-in replacement for hand-specified obstacle geometry.
Long-term robot operation in evolving environments requires object-level understanding that persists across repeated revisits. Existing systems either overwrite history to maintain an up-to-date map or store semantic snapshots without consistent cross-session object identity, resulting in temporal amnesia: the systematic loss of object history that prevents answering queries such as "Where has the green chair been across all sessions?" We propose LT-Mem, a volatility-aware memory evolution framework that unifies spatially aligned instance-level 3D perception with volatility-conditioned temporal reasoning. First, a multi-session SLAM backbone provides spatially aligned per-object observations across sessions. Second, a reasoning layer governs how object memory evolves: deterministic evidence scoring preserves cross-session identity, and a volatility-aware policy selects among overwrite, hold, and multi-hypothesis actions based on each object's dynamics. Third, the resulting Tri-Memory structure (Live, Delta, Meta) preserves both current states and event histories, enabling longitudinal object-centric reasoning. We further introduce LT-VQA, a dataset and evaluation suite comprising multi-session recordings, persistent identity annotations, and temporal QA pairs. Experiments show that LT-Mem consistently outperforms baselines across all metrics while consuming an order of magnitude fewer tokens, and ablations confirm that gains are driven by the structured memory architecture rather than LLM capacity.
Brachiation is a form of locomotion in which primates move primarily using their arms, enabling traversal in environments without footholds. However, this motion requires highly coordinated whole-body movement and precise timing control for bar grasping and release. As a result, achieving robust behavior on life-sized robotic platforms remains challenging. In this study, we present a reinforcement learning-based method to realize brachiation on a life-sized dual-arm robot. The core of the proposed approach is Waypoint-Guided Reinforcement Learning (WGRL), a learning framework for inducing non-linear and complex motions. For high-difficulty tasks where imitation learning data are unavailable, WGRL guides behavior acquisition by sparsely specifying waypoints for the end-effector trajectory, while whole-body motion is generated through reinforcement learning. In addition, by integrating the waypoint-following guidance with rewards based on task success and mechanical energy, and training in an environment designed for Sim-to-Real transfer, the proposed method achieves both forward progression and motion stability. The acquired behavior is evaluated through Sim-to-Sim experiments under monkey-bar environments with geometric variations and hardware experiments, confirming robust brachiation including failure recovery behavior. This study provides effective learning design guidelines for realizing arm-based locomotion on life-sized robotic hardware and expanding the traversable workspace of robots.
Learning from demonstration is a promising approach for dexterous manipulation, but collecting high-quality contact-critical demonstrations remains difficult with low-cost teleoperation hardware. We present ViHaTeleop, a lightweight (0.7 kg), low-cost (\$550) visual-haptic teleoperation system with SLAM-based wrist tracking, camera-based hand tracking, and finger-wise vibrotactile feedback through Linear Resonant Actuators (LRA). The system includes several design choices (LED illumination, fisheye hand camera, and tactile-aware retargeting constraints) and is deployed on Franka + LEAP Hand + 9DTact in both real and simulated environments. Under matched with/without-haptic conditions with nine participants across six contact-critical tasks, haptics improved success rates across all tasks (+2.2 to +15.6 percentage points), while completion-time effects were task-dependent. Subjective ratings showed significant gains in contact clarity and grasp confidence in both simulation and real-world settings (Wilcoxon signed-rank, $p<0.05$). We also integrate a lightweight depth-camera-based tactile proxy in Isaac Sim, enabling a full pipeline from multi-modal demonstration collection to visual-tactile policy training. Preliminary downstream validation by training visual-tactile policies from collected demonstrations shows tactile cues benefit contact-critical subtasks (peg-in-hole: +17 percentage points over vision-only).
Contact-rich manipulation poses a discrete question and a continuous one at once, namely which contacts are active and how to move while they hold. The two are coupled by a change of dimension, since each contact that a robot maintains confines its motion to a lower-dimensional manifold. We make that coupling the explicit object of planning by observing that a contact mode is not merely analogous to a stratum of the configuration space; it is one. A plan is then a walk over strata whose within-stratum segments are geodesics. On two contact-rich manipulation tasks in simulation, pushing a T-shaped block around obstacles and reorienting a cube in a dexterous hand, our planner returns solutions within seconds with no mode, contact sequence, or stratum given in advance.
Long-horizon robotic manipulation fundamentally relies on persistent spatial memory. However, existing 3D memory systems function merely as passive recorders: they store observations using fixed, hand-crafted rules, treating every scene element--whether a critical grasp target or an irrelevant background wall--with equal importance. In this paper, we propose a paradigm shift from passive storage to active, task-driven spatial memory. We argue that a robot's memory should not simply record what it sees, but actively learn how to remember--discovering which objects to track precisely, how aggressively to update them, and what to discard, all learned end-to-end without hand-designed rules. Crucially, this active paradigm is realized by unifying memory update and readout as two sides of the same cognitive process, enabling bidirectional flow where task needs shape update strategies and vice versa. To instantiate this vision, we introduce GaussMemory, which leverages 3D Gaussian Splatting as a persistent geometric substrate. On LIBERO, GaussMemory outperforms MemoryVLA on Goal and Long-10; on VLABench, it surpasses $π_0$-FAST by +5.2% (Track 1) and +6.0% (Track 6).
Recent 3D Gaussian Splatting (3DGS) has enabled efficient photorealistic view synthesis and is rapidly being adopted in simultaneous localization and mapping (SLAM) systems for online mapping. In these systems, a Gaussian map must be expanded and refined incrementally while tracking runs in real time, so initialization and density control directly determine where limited computation and iterations are spent. This contrasts with offline 3DGS reconstruction, where such heuristics can be amortized over long optimization schedules. However, most 3DGS-SLAM pipelines inherit initialization and density-control heuristics from offline reconstruction, which can become brittle under the strict per-keyframe optimization budgets and incremental map growth of online SLAM. In this work, we revisit these heuristics in a decoupled 3DGS-SLAM setting and propose three geometry-aware methods that operate in the mapping thread: transmittance-preserving densification, camera-aware scale initialization from depth and intrinsics, and error-guided densification that focuses new primitives on high-residual regions. Our results show consistent improvements in rendering quality with negligible overhead, highlighting the coupling between photometric residuals and pose uncertainty in online SLAM. We will open-source our code to the community to foster growth and validate reproducibility.
Social robots are expected to operate across diverse environments, where similar arrangements can imply different socially appropriate actions, e.g., starting a conversation may be acceptable in a crowded home but disruptive in an office meeting. Because such norms and environments cannot all be anticipated in advance, robots require continual learning (CL) to adapt from sequential experience while retaining previously acquired knowledge. Prior work has studied CL for generating socially appropriate robot actions, but it has not addressed domain-incremental settings in which the robot incrementally encounters diverse contexts (e.g., living room, meeting room, office, hallway), where both environmental (e.g., whether the space is open or cluttered with furniture) and social cues (e.g., how people or other agents are positioned around the robot) jointly shape the appropriateness of robot actions. We address this gap with the Explicit Disentanglement Dual-Branch (EDD) framework. EDD explicitly separates environmental and social-agent related knowledge and uses replay-based rehearsal to mitigate forgetting while learning the appropriateness of robot actions (e.g., cleaning, serving, starting a conversation) across several indoor domains. Experiments show that EDD outperforms several state-of-the-art baselines, and ablation studies further evaluate different disentanglement strategies and the sensitivity to domain ordering. Our code is publicly available at https://github.com/Cambridge-AFAR/Mind-the-Context.git.
Training and validation of Embodied AI for social navigation critically depends on realistic simulation environments, yet many current approaches fail to find a balance between realism and simulability. We propose D3D-GEN, a novel world generation system that combines a domain agent with a retrieval-augmented generation (RAG) pipeline grounded in that domain. Our system enables users to rapidly generate domain-grounded, fully interactive 3D worlds by automating both the collection of domain knowledge and the synthesis of realistic floorplans and object placements, without dependence on any fixed 3D model database. Given a domain description prompt, the research agent collects publicly accessible domain-specific data and constructs a persistent domain database. Using this database, our RAG pipeline generates plausible floorplans and object placements by dynamically querying a user-provided semantic database, which can be easily extended or modified. The output is a fully interactive 3D world loadable by the popular simulators Isaac Sim and Gazebo. With our approach, we have built databases for several common domains (indoor residential, hospital, office) and generated dozens of distinct, plausible simulation environments for each domain. We present D3D-GEN with a local web frontend that facilitates rapid, interactive world generation for robot simulation.
Depth estimation from thermal images is highly valuable for robotic applications in adverse conditions, such as nighttime and rainy weather. Recent studies have sought to transfer knowledge from RGB-based foundation models to thermal modalities, yet the rich hierarchical representations these models encode remain underutilized. To address this limitation, we propose RGB-HS, a novel framework for thermal-image depth estimation that leverages hierarchical supervision from an RGB-based foundation model. Specifically, we first replace the baseline thermal encoder with a foundational model and introduce a parallel RGB branch that also employs a foundational model as an encoder of the same architecture, taking RGB images as input. The alignment is then performed across multiple levels between the tokens of the two encoders, allowing the thermal student branch to capture both structural precision and semantic abstraction from the RGB teacher branch. Furthermore, we introduce verification to refine the alignment process by weighting tokens from the RGB branch based on RGB image quality. Extensive experiments on the popular benchmark demonstrate that RGB-HS achieves competitive performance and more effectively exploits the representational capacity of RGB-based foundation models for depth estimation on thermal images.
Robots operating in dark or poorly lit environments rely on onboard lights, which often produce uneven illumination that degrades downstream perception tasks. Prior approaches based on 2D image enhancement lack reliable supervision and fail to preserve multi-view geometric consistency. To address these limitations, we extend Dark Gaussian Splatting (DarkGS) toward a more accurate and flexible relightable 3D reconstruction framework. First, we eliminate the need for explicit light parameter calibration by jointly optimizing lighting parameters within the Gaussian Splatting framework. Second, we introduce a low-frequency illumination model based on spherical harmonics (SH) to capture spatially varying residual and ambient lighting effects. Third, we incorporate an MLP-based Bidirectional Reflectance Distribution Function (BRDF) to model non-Lambertian reflectance. Experiments on synthetic and real-world datasets demonstrate that our method effectively mitigates illumination artifacts while improving rendering quality and quantitative performance over prior approaches. We further validate its benefits for robotic perception through a downstream task.
Vision-Language-Action(VLA) models map camera images and language instructions directly to motor commands through a single autoregressive transformer. In real-time control, they still spend substantial compute recomputing key-value(KV) representations for visual tokens that barely change across neighboring frames. Recent work such as VLA-Cache reduces that cost by reusing KV states for visually static patches, but its policy relies only on observation-space heuristics and does not account for the model's own uncertainty. We propose Gated VLA-Cache, a lightweight, training-free extension that augments visual-similarity caching with neural introspection. The method monitors the logit margin between the top two predicted action tokens, a zero-cost confidence signal available during decoding. When the margin drops below a threshold, the cache is invalidated and a full recompute is triggered. Evaluated on four LIBERO benchmark suites with both OpenVLA and OpenVLA-OFT, Gated VLA-Cache improves reliability when blind caching hurts. On LIBERO-Goal and LIBERO-Long, it recovers over 100% of the lost accuracy while retaining 80% of the compute savings.
Bimanual dexterous grasping of large objects is a critical challenge in robotic manipulation. However, most existing studies focus on sequential manipulation rather than cooperative grasping, and methods addressing such bimanual tasks have largely been limited to simulation. These limitations stem from the difficulty of acquiring full 3D object models and generating physically plausible grasping actions. To fill this gap, we propose a real-world bimanual grasping framework that includes: a multimodal dataset capturing joint angles, visual observations and force signals; a Denoising Diffusion Probabilistic Model (DDPM)-based module that generates joint-level grasp configurations from segmented point clouds; and an execution strategy that integrates motion planning with online grasp refinement to ensure physical stability and feasibility. Our approach enables the synthesis of executable bimanual grasps from single-view inputs, reducing dependence on complete 3D object models and ensuring stable real-world performance. Experiments on a dual-arm robot demonstrate high success rates across unseen objects with varying geometries and poses, and ablation studies confirm the contributions of key components of our system.
Following a target human in crowded environments involves an inherent conflict between staying close to the target and navigating safely among surrounding pedestrians and obstacles. This conflict becomes more severe in dense scenarios, where aggressive following risks collisions and conservative margins lead to target loss, especially when pedestrian behaviors are unfamiliar or unpredictable. Existing reinforcement learning (RL) methods typically encode these competing objectives into a single dense reward, but the resulting proximity-safety balance is implicit and difficult to adjust across conditions. To address this, we decompose the human-following task into a sparse task reward and independent cost constraints within a multi-constraint RL formulation, where each constraint is managed through cost thresholds with direct behavioral meaning rather than implicit reward weight ratios, allowing explicit and tunable control over the trade-off. We further quantify the prediction uncertainty of human motions and integrate these estimates into the RL costs to enhance safety under unpredictable conditions. Extensive experiments across both in-distribution and out-of-distribution settings demonstrate that our method achieves an effective proximity-safety balance compared to baselines. Real-robot deployment further validates the feasibility of our method in real-world scenarios. More details are available on our project page: https://nav-ps-balance.github.io/.
Human-Robot Collaboration (HRC) plays a vital role in dynamic, high mix, low volume industrial scenarios such as remanufacturing, which frequently face workcell rearrangements. Traditional setups are constrained by power and data cabling, restricting modularity and reconfigurations, while the selection of commercial wireless devices suitable for real-time perception and safe collaboration are limited in availability. This paper presents a highly flexible, wireless, 5G-based system that serves as a versatile experimental testbed for applications including remanufacturing, operator training, and user studies. To eliminate infrastructure barriers, the workcell integrates a novel battery-powered, multi-sensor platform prototype. Additionally, to support operator safety and system adaptability across environmental shifts, the system integrates a computer vision module for object detection and pose estimation, further augmented for robust hand recognition. Trained on synthetic and real data, the model reliably detects oriented grasping poses and human hands across varying lighting and background conditions (with an mAP@50-95 of 97.74 +- 0.10% and a mean inference time of 12.5 ms). Offloading these computationally intensive tasks to the edge via 5G, the proposed architecture contributes to resolving the bandwidth-latency trade-off. To demonstrate portability, the system was implemented in both Hungary and Norway, and was evaluated across a combination of public and private, Standalone and Non-Standalone 5G infrastructures. The performed network experiments produced results in round-trip response times down to 12 ms in case of compatible network-device pairings, suitable for safe, adaptive HRC. However, these measurements also revealed practical limitations related to interoperability in current 5G deployments that should be addressed in future works.
Traffic sign recognition (TSR) models based on deep neural networks achieve strong clean-data performance but remain vulnerable to physically realizable adversarial attacks, including shadow perturbations, natural-light interference, and printed patches. Existing defenses often improve robustness against one attack type while degrading performance on others, and can reduce clean accuracy. We propose LAMDA (Language-Anchored Model for Direction Alignment), a training framework that transfers language-grounded structure into TSR models without using adversarial examples or adding inference-time overhead. LAMDA builds two fixed prototype banks from VLM-generated sign descriptions and class names using a frozen OpenCLIP text encoder, and uses them to supervise visual features through two complementary auxiliary losses during training. At inference, the adapter and prototype banks are discarded, leaving a standard backbone and classifier. Evaluated on GTSRB and LISA across four backbones and three physical attack types, LAMDA is the only method among ten evaluated that consistently improves robustness across all attack-backbone-dataset combinations, with gains of up to +12.5 pp under shadow attacks and +13.2 pp under natural-light attacks, while preserving or improving clean accuracy in nearly all cases.
Hardware failures require legged robots to rapidly reorganize coordination and gait timing to maintain stability and mobility. This is particularly challenging for larger quadrupeds, where increased mass and tighter actuation limits reduce the feasibility of aggressive, high-frequency compensation strategies often observed on smaller platforms. In this work, we propose a deep reinforcement learning approach for fault-tolerant locomotion under actuator power loss. The method employs an asymmetric actor-critic architecture in which the critic has access to privileged information during training, while the actor learns to reconstruct a corresponding latent representation from proprioceptive observations. We introduce a latent-alignment loss that encourages consistency between actor and critic representations. Additionally, we augment the action space with a learnable gait frequency parameter, enabling adaptive gait timing in response to terrain variations and actuator degradation without predefined faulty-leg strategies. The approach is validated in high-fidelity simulation on uneven terrain and real-world experiments on flat ground using a 68 kg quadruped robot.
LiDAR serves as a primary sensing modality for robots operating in outdoor environments. However, the performance of deep learning models in this domain is severely limited by the scarcity of labeled data, a direct result of the high cost of 3D annotation. Self-supervised learning addresses this scarcity by learning general-purpose features from unlabeled data. In this work, we present a multi-modal, multi-teacher distillation framework for self-supervised learning on outdoor LiDAR point clouds. Building upon the Sonata architecture, we introduce Vernata, consisting of three extensions: sparse view augmentation to improve robustness against varying point densities, a memory bank mechanism to stabilize resource-constrained training, and cross-modal distillation utilizing dense, high-resolution 2D image features to enable fine-grained semantic guidance. We evaluate our method on the GrandTour, TartanGround, and Waymo datasets, as well as data collected from our own robotic platforms. Our experiments demonstrate a significant performance improvement over Sonata baselines, yielding mIoU scores of 54.7 on TartanGround (+5.9 points, +12.1%) and 57.1 on Waymo (+7.3 points, +14.7%). Finally, we show that the self-supervised approach maintains strong performance even in reduced-modality settings (lacking color or normals), achieving competitive mIoU scores of 49.4 and 50.2 on the respective datasets.
Robot swarms utilize many independent limited-sensing agents to produce complex emergent behaviors without requiring centralized control. However, little research explores how agents can infer swarm-level behavior from purely local perception, a capability critical for detecting faults and behavior changes. In this paper, we introduce Synchronized Swarm Behavior Classification (SyncSBC), which combines improvements in machine learning and distributed consensus to classify collective swarm behavior and synchronize swarm decision-making in an entirely decentralized manner. We show that SyncSBC achieves high classification accuracy and low synchronization delay, making it suitable for real-world deployment. Finally, we use SyncSBC to demonstrate two promising swarm applications on real robots where we show that swarms utilizing SyncSBC can accurately identify anomalies in robot behavior and autonomously coordinate collective changes in swarm behavior. Videos, code and supplemental experiments are available at https://sites.google.com/view/sync-sbc/home.
Safe control has been widely studied in various safety-critical applications, for instance, autonomous driving. In order to ensure the autonomous vehicle does not collide with other vehicles, it is essential to obtain an accurate expectation of surrounding vehicles' behavior and react adaptively. Instead of assuming fully cooperative and homogeneous vehicles using the same safety-critical controllers, recent works have been exploring different data-driven approaches to model the neighboring vehicles' underlying controllers with observed data. However, existing works either suffer from 1) the inter-vehicle influence during the multi-vehicle interaction, which makes it hard to determine the causality of surrounding vehicles' behavior in controller modeling, or 2) being dominated by the worst-case analysis, which may lead to overly conservative behavior. In this paper, we extend the prior work on Parametric-Control Barrier Function (Parametric-CBF) to multi-robot interactions with embedded causality inference to explicitly reason over the inter-vehicle influence. Given the learned Causality-based Parametric-CBF, we present an adaptive safety-critical controller that allows the ego vehicle to safely react to surrounding vehicles with the learned expectation. We demonstrate that by leveraging the motion flexibility among multi-vehicle systems, task efficiency can be greatly improved in various interaction-intensive scenarios.
Safe navigation often relies on well-defined conditions based on the shape of robots and obstacles, and can be challenging when they have irregular geometries. While Control Barrier Functions (CBFs) offer an efficient mechanism to enforce safe set forward invariance, common shape surrogates (e.g., spheres or super-ellipsoids) either are overly conservative in unstructured scenes or require many local primitives, which inflates constraint counts and degrades real-time performance. In this paper, we introduce a novel geometry-aware Control Barrier Function (CBF) based on Bernstein-Polynomial Signed Distance Fields (BP-SDFs). It provides a unified way to represent the obstacles and robots, so as to represent the barrier function with a unified minimum distance. Benefiting from the differentiability of the Bernstein polynomials, one can easily enforce the control constraints in a closed loop. We validate the method's efficiency and performance to guarantee safety in single-robot navigation and heterogeneous multi-robot collision avoidance via simulations under different environments.
Robots operating in human-centric environments must be both robust to disturbances and provably safe from collisions. Achieving these properties simultaneously and efficiently remains a central challenge. While Dynamic Movement Primitives (DMPs) offer inherent stability and generalization from single demonstrations, they lack formal safety guarantees. Conversely, formal methods like Control Barrier Functions (CBFs) provide provable safety but often rely on computationally expensive, real-time optimization, hindering their use in high-frequency control. This paper introduces SafeDMPs, a novel framework that resolves this trade-off. We integrate the closed-form efficiency and dynamic robustness of DMPs with a provably safe, non-optimization-based control law derived from Spatio-Temporal Tubes (STTs). This synergy allows us to generate motions that are not only robust to perturbations and adaptable to new goals, but also guaranteed to avoid static and dynamic obstacles. Our approach achieves a closed-form solution for a problem that traditionally requires online optimization. Experimental results on a 7-DOF robot manipulator demonstrate that SafeDMPs is orders of magnitude faster and more accurate than optimization-based baselines, making it an ideal solution for real-time, safe, and collaborative robotics.
Model Predictive Control (MPC) is widely adopted for agile multirotor vehicles, yet achieving both stability and obstacle-free flight is particularly challenging when a payload is suspended beneath the airframe. This paper introduces a Safety Enhanced Passivity-Based Nonlinear MPC (SEP-NMPC) that provides formal guarantees of stability and safety for a quadrotor transporting a slung payload through cluttered environments. Stability is enforced by embedding a strict passivity inequality, which is derived from a shaped energy storage function with adaptive damping, directly into the NMPC. This formulation dissipates excess energy and ensures asymptotic convergence despite payload swings. Safety is guaranteed through high-order control barrier functions (HOCBFs) that render user-defined clearance sets forward-invariant, obliging both the quadrotor and the swinging payload to maintain separation while interacting with static and dynamic obstacles. The optimization remains quadratic-program compatible and is solved online at each sampling time without gain scheduling or heuristic switching. Extensive simulations and real-world experiments confirm stable payload transport, collision-free trajectories, and real-time feasibility across all tested scenarios. The SEP-NMPC framework therefore unifies passivity-based closed-loop stability with HOCBF-based safety guarantees for UAV slung-payload transportation.
Shared autonomy blends operator intent with autonomous assistance. In cluttered environments, linear blending can produce unsafe commands even when each source is individually collision-free. Many existing approaches model obstacle avoidance through potentials or cost terms, which only enforce safety as a soft constraint. In contrast, safety-critical control requires hard guarantees. We investigate the use of control barrier functions (CBFs) at the inverse kinematics (IK) layer of shared autonomy, targeting post-blend safety while preserving task performance. Our approach is evaluated in simulation on representative cluttered environments and in a VR teleoperation study comparing pure teleoperation with shared autonomy. Across conditions, employing CBFs at the IK layer reduces violation time and increases minimum clearance while maintaining task performance. In the user study, participants reported higher perceived safety and trust, lower interference, and an overall preference for shared autonomy with our safety filter. Additional materials available at https://berkguler.github.io/barrierik.
Diffusion policies (DPs) achieve state-of-the-art performance on complex manipulation tasks by learning from large-scale demonstration datasets, often spanning multiple embodiments and environments. However, they cannot guarantee safe behavior, requiring external safety mechanisms. These, however, alter actions in ways unseen during training, causing unpredictable behavior and performance degradation. To address these problems, we propose path-consistent safety filtering (PACS) for DPs. Our approach performs path-consistent braking on a trajectory computed from the sequence of generated actions. In this way, we keep the execution consistent with the training distribution of the policy, maintaining the learned, task-completing behavior. To enable real-time deployment and handle uncertainties, we verify safety using set-based reachability analysis. Our experimental evaluation in simulation and on three challenging real-world human-robot interaction tasks shows that PACS (a) provides formal safety guarantees in dynamic environments, (b) preserves task success rates, and (c) outperforms reactive safety approaches, such as control barrier functions, by up to 68 % in terms of task success. Videos are available at our project website: https://tum-lsy.github.io/pacs.
Reinforcement learning (RL), while powerful and expressive, can often prioritize performance at the expense of safety. Yet safety violations can lead to catastrophic outcomes in real-world deployments. Control Barrier Functions (CBFs) offer a principled method to enforce dynamic safety -- traditionally deployed online via safety filters. While the result is safe behavior, the fact that the RL policy does not have knowledge of the CBF can lead to conservative behaviors. This paper proposes CBF-RL, a framework for generating safe behaviors with RL by enforcing CBFs in training. CBF-RL has two key attributes: (1) minimally modifying a nominal RL policy to encode safety constraints via a CBF term, (2) and safety filtering of the policy rollouts in training. Theoretically, we prove that continuous-time safety filters can be deployed via closed-form expressions on discrete-time roll-outs. Practically, we demonstrate that CBF-RL internalizes the safety constraints in the learned policy -- both enforcing safer actions and biasing towards safer rewards -- enabling safe deployment without the need for an online safety filter. We validate our framework through ablation studies on navigation tasks and on the Unitree G1 humanoid robot, where CBF-RL enables safer exploration, faster convergence, and robust performance under uncertainty, enabling the humanoid robot to avoid obstacles and climb stairs safely in real-world settings without a runtime safety filter.
Control Barrier Functions (CBFs) are a powerful tool for ensuring the safety of autonomous systems, yet applying them to nonholonomic robots in cluttered, dynamic environments remains an open challenge. State-of-the-art methods often rely on collision-cone or velocity-obstacle constraints which, by only considering the angle of the relative velocity, are inherently conservative and can render the CBF-based quadratic program infeasible, particularly in dense scenarios. To address this issue, we propose a Dynamic Parabolic Control Barrier Function (DPCBF) that defines the safe set using a parabolic boundary. The parabola's vertex and curvature dynamically adapt based on both the distance to an obstacle and the magnitude of the relative velocity, creating a less restrictive safety constraint. We prove that the proposed DPCBF is valid for a kinematic bicycle model subject to input constraints. Extensive comparative simulations demonstrate that our DPCBF-based controller significantly enhances navigation success rates and QP feasibility compared to baseline methods. Our approach successfully navigates through dense environments with up to 100 dynamic obstacles, scenarios where collision cone-based methods fail due to infeasibility.
Soft robots offer safe and adaptive interaction with humans and unstructured environments through their inherent ability to deform and comply. Pneumatic actuators are one way to build soft robots. They are typically made from soft silicone materials and are especially effective for driving such systems, enabling smooth and adaptable motion. However, their compliant nature also makes them vulnerable to mechanical failures like punctures and tears, limiting practical deployment. To address this, we propose a puncture detection system for soft actuators using motion data from a single inertial measurement unit. Extracted features are used to train anomaly detectors for puncture detection and non-linear models to estimate severity. We also introduce a multi-chamber pneumatic soft bending actuator capable of diverse configurations via selective chamber inflation. Our algorithm identifies the punctured chamber and provides a severity score using a chamber perturbation scheme. Anomaly detectors are trained on normal operation data and detect damage through reconstruction errors, while severity is estimated by a separate model trained under slightly modified conditions. Finally, we demonstrate a failure recovery strategy to maintain actuation force post-failure. This approach enhances the reliability and safety of soft robotic systems through real-time, data-driven damage detection.
This paper presents a novel framework designed to enhance key object identification in autonomous driving. Existing methods primarily focus on either detecting objects independently or leveraging visual relationships, but they do not explicitly consider the ego vehicle's perspective in determining object importance. To address this gap, we propose a structured approach that integrates a virtual ego-vehicle representation and a modular object state predictor, enabling a more accurate estimation of object behaviors relative to the ego-vehicle. Subsequently, our framework employs spatial-temporal reasoning to refine key object identification, prioritizing objects based on their states and relative spatial information rather than relying solely on visual relationships. Experimental results on real-world driving datasets demonstrate the effectiveness of our approach in accurately detecting critical objects in complex traffic environments.
Can interactive vision-and-language agents learn not just what to say but also \textbf{\textit{when}} to say it? Current language models rarely plan over whether and when to realize a real-time response to a user. However, providing accurate and timely support for human decision-making, such as when guiding visually impaired individuals through urban environments, requires careful real-time responsiveness--poorly timed responses can distract users or add unnecessary cognitive load. As a machine intelligence challenge for Multimodal Large Language Model (MLLM)-based agents, we introduce a large-scale multimodal benchmark for an egocentric, assistive navigation task in complex outdoor environments. Using this benchmark, we uncover a fundamental limitation of off-the-shelf MLLMs in delivering safe and time-sensitive navigation instructions, even with model fine-tuning on substantial amounts of data. We then demonstrate that a simple yet effective modification of the model, including direct supervision to predict the underlying reason for each instruction, yields significant performance gains across open-loop, closed-loop, and sim-to-real generalization settings. However, our analysis highlights persistent challenges in temporal reasoning, safety-critical object awareness, and relational and distance understanding. To advance the development of scalable assistive agents, we will release our simulation, benchmark, and code (available at the project website: https://timeli-icra.github.io/).
Labelling vision datasets, especially for segmentation tasks, is a laborious and costly process that stymies novel developments in agricultural robotics. In this paper, we present DropClick, a click-guided segmentation tool that simplifies the annotation process. Our system utilises single-click inputs on objects to generate pseudo-labels, which can replace manual annotations. DropClick stands out as it is a semi-automated approach and does not require a click for every object in the scene. It can therefore further reduce the required amount of user input drastically. We evaluate our method on two challenging agricultural robotic datasets, SB20 and BUP20 for plant and fruit segmentation, respectively. DropClick is first trained on a small subset of just 5 images from the original training data. This DropClick model can then be deployed as a one-click segmentation system and achieves comparable or higher performance than other one-click methods achieving an mIoU of 70.0 and 72.6 points, for SB20 and BUP20 respectively. DropClick then excels at maintaining high performance when clicks are not given (e.g. dropped); when 50% of the clicks are missing it still maintains an mIoU of 68.9 and 71.3 points, for SB20 and BUP20 respectively. We validate DropClick as a pseudo-labelling approach by taking its outputs to train a Mask2Former instance-based segmentation model in a semi-supervised manner. In this process, partially removing user input from DropClick yields similar high performance when compared to providing all clicks, at 70.1 vs 70.7 points AP50 for SB20 and no difference for BUP20 at 77.0 for both models; at the same time saving 46.3% of total input for SB20 and 31.9% for BUP20.
Existing Human-Robot Interaction (HRI) literature has focused on identifying and structuring errors, failures, conflicts, and knowledge issues (called in this work as contradictions) in domain-specific dialogue-based interactions. However, there is still lack of a formal computational framework to represent and define these contradictions, interoperable and usable across HRI and human-agent interaction (HAI) domains. Thus, this research project aims to capture, represent, and evaluate the notion of (1) dialogue-based collaborative interaction and (2) related contradictions in a foundational ontology. METHONTOLOGY, a systematic approach to build domain-independent ontologies was applied. In the conceptualisation stage of the presented ontology, concepts and models from Activity Theory were used. Preliminary results presented in this short article are: (i) Natural language definitions of dialogues and related contradictions in HRI, (ii) Set Theoretic definitions of dialogues and contradictions, and (iii) First Order Logic (FoL) formulation of the contradiction concepts and three novel principles guiding dialogue-based interactions between humans and robots. In summary, we report on ongoing work to develop a foundational ontology based on Activity Theory called Activity Theory-based foundational ontology (ATFOt) to capture and represent the notion of contradictions in HRI.
Learning from demonstration (LfD) methods enable non-expert end users to teach robots novel skills without explicit programming. However most evaluations of the usability of LfD with non-experts has been conducted in controlled laboratory environments with a robotics experimenter present. In this work we identify non-expert end users' key barriers when teaching robots via demonstration without live robotics expert feedback in a home environment. In our human subjects experiment we support the non-expert end users through two forms of demonstrator guidance developed in prior work: pre-training and adaptive feedback. Towards the ecological validity of the evaluation, we conduct this experimentation over multiple visits, with a population of care providers. Finally, we propose to open source the resulting LfD dataset of care providers teaching a robot assistive tasks over multiple visits to a home environment.
Current Vision-based SLAM systems fail catastrophically when motion blur corrupts the visual input, as they attempt the ill-posed inverse problem of recovering sharp content from degraded observations. We present MotionGS-SLAM, which fundamentally reimagines motion blur handling through a paradigm shift: rather than removing blur artifacts, we reformulate the challenge as a well-constrained forward problem that generatively models blur formation within the rendering pipeline. By leveraging event cameras' microsecond temporal resolution and immunity to motion blur, we introduce a novel event-modulated Gaussian kernel that dynamically adapts each Gaussian's rasterization based on precise motion cues. Our dual-modulation mechanism transforms 2D Gaussian projections from isotropic dots into anisotropic, motion-aligned elliptical brush strokes (spatial modulation) while adaptively varying exposure integral sampling density based on local velocity (temporal modulation). This physics-based approach enables joint optimization of intra-exposure camera trajectories and 3D scene geometry through blur-aware photometric and event-based constraints. Extensive experiments demonstrate significant improvements over state-of-the-art methods in trajectory accuracy and map quality under severe high-motion conditions.
Service robots operate in household environments shared with humans, pets, and everyday objects, where they are highly susceptible to failures such as software crashes, hardware degradation, or unpredictable interactions. While roboticists strive to minimize failures, some remain inevitable, making it critical to mitigate their potential consequences for safe and reliable deployment. This paper introduces a novel safety formulation that evaluates both the probability of impactful interactions between robots and surrounding entities during failures, and the severity of their outcomes. By quantifying the impact of failures on different entities, our approach enables robots to make informed planning decisions that balance safety with task efficiency. To support systematic evaluation, we also present FailBench, a MuJoCo-based simulation framework for studying robot-environment interactions under diverse failure modes, including sensing issues and actuator malfunctions. Together, our safety formulation and FailBench provide a foundation for developing safer and more robust motion plans and learned policies in real-world household environments.
Manipulation involving rigid-deformable interactions, such as hanging clothes or dressing humans, is common in daily life, making it essential for household robots. Compared to single-object manipulation or interactions between rigid bodies, these tasks are particularly challenging due to the rich multi-point contacts and the complex dynamics of the deformable bodies during interaction. Therefore, object-centric representations such as 6D poses or structural points without task-specific information become insufficient for these interactions. In this work, we propose a hybrid correspondence-based representation tailored for rigid-deformable interactions. First, to capture intricate interaction information, we introduce structure-, task-, and interaction-aware sparse keypoints. The keypoints are generated based on the global structures of both rigid and deformable objects, and filtered by their local interaction contacts. However, tracking these sparse keypoints through the interaction remains difficult due to the high-dimensional dynamics of deformable objects. Therefore, we further construct dense correspondences on the deformable objects for accurate keypoint tracking throughout the manipulation. This hybrid design combines the advantages of both representations: sparse keypoints encode rich, task-specific information for fine-grained manipulation, while dense correspondences ensure efficient tracking and generalization to novel deformations, shapes, and scenarios. Together, they enable one-shot transfer to new tasks with minimal demonstrations. Extensive experiments demonstrate the effectiveness and broad applicability of our method.
Contact planning in robotics requires models that are both computationally efficient and physically accurate. Sphere-based robot representations satisfy the first requirement by enabling fast collision checking and differentiable geometry, but sacrifice physical accuracy by relying on point contact which cannot capture contact patch area, pressure distributions, rotational stiffness, or frictional moments. We introduce Compliant Sphere Lattice Contact (CSLC), a distributed contact model that operates natively on sphere representations by modeling the robot interface as a compliant lattice of surface spheres connected through anchor and lateral springs. When pressed against an object, the lattice deforms to produce a spatially distributed contact patch that improves the physical accuracy of sphere-based contact. We validate CSLC across two independent solvers and show preliminary results demonstrating contact patch formation and improved grasp stability.
The introduction of new technologies, such as surgical robots, is driving the vision of a connected, smart operating room (OR). However, realizing this vision requires a deep understanding of surgical workflows, which relies on realistic datasets capturing the actions of all OR personnel from both full room and surgical field perspectives. Acquiring such data in real ORs is prohibitively challenging due to factors such as ethics committee approvals, limited space for camera installation, and sterility regulations preventing the use of tracking markers. We present a step-by-step methodology for re-enacting complete surgical procedures in a reconstructed OR. This approach enables the creation of repeatable and annotatable workflow datasets for training activity recognition models, generating scene graphs, and formalizing surgical process models. Developed for robot-assisted ophthalmic surgery, our methodology combines expert consultation, structured workflow formalization, OR reconstruction, role-based training, real OR observation, and iterative recording with post-take debriefing. We provide concrete recommendations to allow other research groups to seamlessly adopt this methodology for their own surgical domains.
While scaling laws for imitation learning have primarily focused on generalization in open-world settings, the relationship between data and precision in closed-world tasks like robotic assembly remains largely unexplored. This paper systematically investigates this relationship and introduces a novel scaling law. We find that to achieve a fixed success rate, the required number of demonstrations $N$ grows super-exponentially as the target precision $P$ approaches a limit $c$. This relationship is accurately captured by the model $\log(N) \propto 1/(P-c)$. Crucially, we reveal that the limit precision $c$ is not a static physical constant of the task but an emergent property of the entire agent system, including its sensors and expert policy. Through experiments on canonical manipulation tasks, we validate this law and demonstrate that improving system components, such as adding a wrist camera or using a more effective expert, measurably lowers $c$, thus expanding the system's achievable precision. Our work provides a new theoretical framework for precision in robotics and a quantitative metric to evaluate system capabilities. Furthermore, these findings provide a practical methodology for guiding the development and debugging of high-precision manipulation systems.
Dynamic object segmentation plays a critical role in many visual applications such as static scene reconstruction from dynamic videos. However, existing optical flow-based methods fail to ensure consistent static/dynamic segmentation along object boundaries, while 3D reconstruction-based approaches are highly sensitive to reconstruction errors. To address these limitations, we present a dynamic object segmentation framework that can generate both precise and complete dynamic masks by integrating multimodal cues including 2D point tracks, 3D reconstruction, and semantic information. We design a network combining Transformer architectures with feature clustering aggregation modules to perform static/dynamic classification of multimodal feature trajectories. It enables the model to adaptively determine which type of feature should dominate based on the characteristics of each scene, while also mitigating the impact of feature degradation. Additionally, we introduce a novel point-query-based SAM post-processing method capable of handling multiple objects within a single mask. Extensive experiments demonstrate that our approach achieves state-of-the-art performance in both dynamic object segmentation and static scene reconstruction tasks.
We provide a novel end-to-end framework for the execution of an assembly operation by two robotic arms, given the digital CAD models of the parts and their desired relative placement in their assembled state. We analyze and demonstrate the advantages of using two robotic arms simultaneously in tight assembly operations, compared to single-arm systems. Our method is implemented in both simulation and using physical robots. It provides theoretical guarantees on execution time and trajectory accuracy, supported by empirical evidence. In particular, we show that coordinated movement of two arms reduces average execution time by more than 50% compared to using a single arm only, produces higher-quality trajectories, and accelerates the search for valid robot placements. Furthermore, we establish bounds on the required dimensions of the robotic cell. Our open source software together with real-life video demonstrations are available in our project page.
Localization is a key task in robot navigation, and many techniques exist for it. In many plausible scenarios, a robot might face unforeseen, dynamic obstacles, rendering any pre-determined map inaccurate for localization. In this work, we propose a robust lifelong localization framework in dynamic planar indoor environments, using the robot's odometry and sparse distance sampling. We demonstrate how distance samples can be used to provide a robust prior on the robot's location. This technique can solve the kidnapped robot problem in real time, up to symmetries. Based on insights from real-world recorded data, we also account for dynamic obstacles. We then fuse this prior, over time, with the odometry to converge to the robot's location. A central property of our method is that it provably converges to the robot's ground truth pose even in large indoor environments when the environment is static. We further show that this guarantee also holds in dynamic environments, as long as the nature of those changes has been correctly learned. We demonstrate the effectiveness of our approach in different real-world indoor environments. In particular, we achieve a localization comparable to SLAM with merely a few (sixteen) distance samples, as opposed to the full LiDAR range. Sufficing with only sparse distance sampling is advantageous in terms of sensor cost, privacy, storage space, and transmission bandwidth.
Shared autonomy enables humans and robots to collaboratively perform tasks by combining human input with autonomous assistance. Most prior work focuses on improving intent inference under a fixed environment, overlooking how workspace design itself affects inference difficulty. We observe that the physical arrangement of objects directly influences the separability of candidate goals under noisy user inputs. We formulate workspace design as an optimization problem and derive a probabilistic correctness guarantee under a bounded noise model. Through simulation experiments across multiple tabletop scenarios, we show that optimized layouts improve goal inference reliability and reduce ambiguity compared to baseline arrangements. We further demonstrate a real-world shared autonomy system that integrates the proposed inference framework. This highlights the role of environment design as a complementary axis for improving shared autonomy systems.
Learning reward functions from human preferences is a widely used approach for aligning robot behavior with user expectations in human-robot interaction. Most existing approaches assume that humans evaluate uncertain outcomes using expected utility (EU), aggregating outcome utilities linearly with their probabilities. However, behavioral evidence shows that humans are systematically risk-sensitive, overweighting rare negative events and exhibiting loss aversion. We study the consequences of this mismatch in social robot navigation, where safety-critical outcomes (e.g., collisions) are rare but highly consequential. We compare EU with Cumulative Prospect Theory (CPT), a nonlinear model of human decision-making, within a Bradley-Terry preference learning framework. Our preliminary experiments show that when preferences are generated by risk-sensitive users, CPT-based learners recover reward functions with substantially lower regret compared to EU-based learners. Our results highlight the importance of modeling human risk sensitivity when learning rewards from preferences over stochastic robot outcomes.
The simultaneous arrival of multiple mobile robots at a target point is crucial for cooperation tasks such as cooperative encirclement, disaster relief, and environmental monitoring. Although the simultaneous arrival problem itself is already complex, the problem becomes more challenging when there are constraints on the robot trajectory curvatures and the speeds are required to be constant (possibly different for different robots), and the control law for robots needs to be distributed. These constraints are typical for a multi-robot system consisting of, e.g., fixed-wing UAVs. To address this challenge, this paper proposes a distributed switching control method based on the maximum consensus protocol. By exploiting the geometric properties of Dubins paths along with optimization principles, a virtual time variable is introduced, and a hybrid control law that combines optimal control with saturated proportional control is designed. Under the proposed control law, each robot is driven to approach the maximum virtual time among its neighbors, thereby achieving simultaneous arrival under some mild conditions. Furthermore, we prove that in certain cases the proposed method attains a theoretically optimal arrival time. The approach is scalable and real-time, with low communication overhead. Its effectiveness and robustness are validated through extensive simulations and experiments.
Conventional robotic grippers face a significant challenge in agricultural automation: the trade-off between compliant, adaptive grasping, pressure balancing among all joints, and high load capacity, often at the cost of high energy consumption. This paper presents a novel hybrid rigid-soft gripper that integrated low-cost, membrane-based pneumatic actuators with 3D-printed dual ratchet-pawl mechanisms to simultaneously achieve shape adaptation, uniform force distribution, and energy-free self-locking. The dual-ratchet structure assembled in an offset configuration significantly increased the angular resolution of the joint locking mechanism. Key experimental results demonstrated the gripper's superior performance: a remarkable maximum load capacity of 4200 g, far exceeding that of conventional soft grippers (45-210 g); more uniform force distribution across object sizes (1.75-35.29% difference ratio) compared to a rigid gripper (56.77-66.44%), with peak contact forces remaining below surface damage thresholds; and a 50.05% reduction in total energy consumption to 42.6 J per grasp cycle, achieved by eliminating the need for continuous pneumatic pressure through the self-locking mechanism, compared to 85.28 J for a conventional soft gripper. The combination of additive manufacturing for ratchets and commercially available materials for pneumatic chambers ensured a low-cost and easily fabricated design. These findings validated that the proposed gripper successfully bridged the gap between soft compliance and rigid reliability, offering a robust and efficient solution for scalable agricultural harvesting and manipulation tasks.
Surgical tissue retraction requires effective manipulation planning under partial and noisy perception. We study state estimation for deformable tissue retraction, where only sparse observations of the tissue surface are available at decision time. We propose a learned state estimator that reconstructs the full deformable mesh state from 40 noisy vertex observations. The estimator combines a multilayer perceptron with a low-dimensional PCA latent representation and is trained using geometry-aware regularization that encourages smooth and physically plausible deformations. We evaluate the approach in a 2D deformable sheet simulation using single-step and multi-step retraction planning. Results show that the learned estimator achieves 98.1% of oracle performance in multi-step retraction while supporting efficient inference. These results demonstrate that learned, geometry-regularized state estimation can support effective deformable manipulation under realistic perception constraints.
This paper presents a framework for multi-session mapping of underwater environments utilizing an affordable action camera. The Visual-Inertial data are augmented by water depth recordings from a dive computer. SVIn2, an open-source VI-SLAM framework, is utilized to generate a trajectory and a sparse reconstruction for each session. Utilizing the keyframes extracted from SVIn2 and the estimated camera poses, a Structure-from-Motion (SfM) framework, COLMAP, is employed for global optimization and to produce a dense reconstruction of the target environment. The presence of calibration targets at fixed locations, when available, is used to estimate the coordinate transformation between different data collection sessions, thus transforming the different sessions into the same coordinate frame. The proposed pipeline is employed for the mapping of a shipwreck off the coast of Barbados. For the first time, both the exterior and the accessible interior parts of the wreck were mapped in two sessions, while a third session employed two cameras with different fields of view.
Assembly action understanding is a key enabler for effective human-robot collaborative assembly, yet it remains challenging due to subtle motions and fine-grained hand-object interactions. We adapt vision-language models (VLMs) to this challenging domain with Compositional Context Fine-Tuning (CCFT), a method that decomposes assembly actions into semantic elements (Verb, Object, Tool) and fine-tunes VLMs to recognize each action element using templated question-answering pairs. This approach ensures near-deterministic outputs. To enable efficient and effective multi-task learning under limited data, a Layer-Partitioned Alternating Training (LP-AT) method is presented, which assigns distinct model layers to recognize specific action elements through element-specific low-rank adapters. LP-AT alternates weight updates across element-specific adapters, reducing cross-task interference while enabling per-adapter hyperparameter optimization. Furthermore, we create HA-ViD-VQA and IKEA-ASM-VQA datasets from existing assembly video datasets. Extensive experiments on these datasets demonstrate that our method consistently outperforms strong action recognition baselines while providing interpretable element-level predictions that can support diverse downstream applications.
Surgical automation is being increasingly studied, yet bridging visual scene understanding with autonomous action planning remains a fundamental challenge. While much research effort has been made on scene perception (e.g., tool recognition and scene segmentation), understanding and predicting actionable possibilities for surgical automation is still underexplored. In this paper, we introduce surgical affordance prediction, which identifies actionable regions for fundamental surgical actions from visual data. Specifically, a novel adaptive feature fusion framework is proposed that leverages the complementary strengths of a self-supervised vision transformer encoder for its superior semantic understanding and a large-scale generative model encoder for its spatially-aware capability. Furthermore, we introduce a hierarchical prompt learning mechanism to adapt to varying procedural contexts. Finally, a scene-guided attention decoder is proposed to focus on critical surgical areas while suppressing background distractions. To validate the effectiveness, we established a new dataset, derived from publicly available surgical datasets with affordance annotations for three basic surgical actions: aspiration, clipping, and retraction. Extensive experiments demonstrate that our approach achieves state-of-the-art performance. Moreover, we validate our framework's applicability for downstream automation on a realistic lung and prostate phantom, and results show that the predicted affordance maps successfully enable autonomous surgical actions.
While recent research has focused heavily on dexterous grasp pose generation, less attention has been devoted to the execution of planned grasps. Under shape and position uncertainty, open-loop execution often yields uncoordinated contacts, causing undesired in-hand object motion and even grasp failures. To address this, this paper proposes a tactile-driven model predictive controller for adaptive and delicate execution of diverse dexterous grasps. Our approach emphasizes multi-contact coordination across both approaching and grasping phases, with three key novelties: (i) coordination-aware phase separation, (ii) arm-hand coordination to compensate for position errors, and (iii) adaptive force coordination to increase contact forces in a balanced manner. An analytical model is employed to relate contact forces to robot joint motions for predictive control. Our formulation imposes no restrictions on grasp types or contact configurations and integrates seamlessly with state-of-the-art grasp pose generation methods. We validate the approach through large-scale simulations involving 15k grasps across 478 objects on three robotic hands, and real-world experiments on 8 objects. Results demonstrate that our method achieves higher grasp success rates and reduced undesired object movements.
Automation in construction is essential for reducing costs and human errors in large-scale projects. We approach the construction progress monitoring from the aspect of detecting changes in construction sites. As construction buildings continue to evolve in geometry and appearance over time, change detection need to be performed from arbitrary camera viewpoints. This necessitates developing 2D Change Detection (2DCD) algorithms that operate robustly across diverse camera perspectives at construction sites. While developing and evaluating such systems is data-intensive, no open-source benchmark dataset exists at the intersection of 2D change detection and construction automation research. Data collection using Unmanned Aerial Vehicles (UAVs) is gaining its popularity in outdoor large-scale surveying. However, in active construction sites conducting drone missions equipped with high-end sensors imposes safety concerns. Flight trajectory and collected camera viewpoints can be significantly limited. To address this critical gap, we introduce iVISION-2DCD, a large-scale synthetically generated dataset from dense LiDAR point clouds with photorealistic input images and accurate ground truth annotations. Our dataset formally defines the problem of viewpoint-robust 2DCD at construction sites and captures the inherent complexities of real-world deployment. In this paper, we present our systematic methodology for synthetic data generation, developing novel view synthesis techniques to overcome bi-temporal alignment and viewpoint diversity challenges, and implementing semi-automated semantic segmentation with change label generation while preserving challenging real-world cases. Benchmark evaluations using state-of-the-art 2DCD algorithms demonstrate that iVISION-2DCD poses novel research challenges for the computer vision and robotics communities.
In this work, we study Compositional Dexterous Functional Object Manipulation (CD-FOM): tasks such as aiming and actuating a spray bottle on a plant or a glue gun on wood, which require both actuating an object's internal mechanism and controlling its pose to apply the object's function to the environment. These tasks pose significant challenges for robots due to the demanding integration of semantic understanding of the object's function, actuation mode, and application area with intricate physical dexterity to manage grasp stability, movement trajectory, and actuation. We introduce CoDex, a zero-demonstration framework that autonomously discovers CD-FOM manipulation strategies. CoDex uses vision-language models (VLMs) to infer semantic constraints from the task and scene. These constraints guide analytic constrained optimization to generate a short list of functional grasp candidates that can be efficiently refined with reinforcement learning to generate full grasp-move-actuate policies transferable from simulation to the real world. We evaluate CoDex on a 7-DoF robot arm with a 16-DoF multi-fingered hand across six CD-FOM tasks involving previously unseen objects with internal mechanisms, including spray bottles, hot glue guns, air dusters, flashlights, and pepper grinders, and their application to unseen target objects, showcasing its ability to autonomously discover and execute complex, physically viable dexterous behaviors without human demonstrations. More information at https://robin-lab.cs.utexas.edu/CoDex/.
Autonomously controlling and handling a vehicle at and beyond its stability limit is a mathematically and computationally demanding task. Prior demonstrations of automated drifting have been limited to research platforms with instantaneous torque delivery and independently actuated wheels, leaving their applicability to production vehicles with actuator latencies and mechanically coupled axles uncertain. To overcome these issues, we design a predictor to compensate for powertrain delays, develop a revised control formulation to accommodate higher actuation latencies as well as a differential coupling on the driven axle, and introduce brake-based velocity stabilization. This paper presents the controller framework, the model extensions, and real-world experimental results. We observe that our controller enables a production sports car with a combustion engine to robustly sustain circular and figure-eight drifts, limiting lateral error to 1.1 m and sideslip overshoot to 0.06 rad despite actuator delays exceeding 250 ms, while mitigating oscillations and maintaining stable path and sideslip tracking. In conclusion, our results establish that autonomous drifting is feasible on production-ready vehicles, opening pathways to advanced safety systems capable of stabilizing cars in scenarios where traditional control fails.
I describe my solution to the LeHome Challenge 2026, an ICRA 2026 competition on bimanual garment folding. The system placed 1st of 62 teams in the online (simulation) round and 2nd in the real-world final. It improves a vision-language-action (VLA) policy with a reinforcement-learning loop. The policy is its own value function: the same network that predicts actions also predicts success, progress, and a few task-relevant future quantities, and those predictions drive advantage estimation, live failure detection, and candidate selection. The work mostly recombines existing RL ideas with engineering and optimization contributions that can be used together as one recipe or individually: AWR + RECAP combined for flow-matching VLA; an asynchronous distributed training / rollout pipeline through HuggingFace Hub; inference-time hyperparameters optimization via Thompson sampling; a sim-to-real recipe with camera-alignment tooling, heavy augmentation and DAgger-like HIL data collection.
With the growing deployment of surveillance systems in factories, offices, and homes, integrating them with robots offers a promising direction for collaborative and efficient task execution. However, existing approaches largely focus on single-robot scenarios and struggle with multi-view collaboration in large-scale environments. In this paper, we present a novel indoor collaborative object navigation dataset built on Habitat-Sim, featuring 206 cameras across 74 floors. The dataset enables systematic evaluation of an agent's ability to exploit multi-view surveillance information. To address the limitations of single-robot perception, we propose SurveilNav, a collaborative navigation framework that integrates active camera scheduling, joint 2D/3D mapping, VLM-based value estimation, and collaborative target verification. By synergizing the robot's dynamic local perception with the static global view of surveillance, this architecture effectively overcomes both the limited perception range of single agents and the inherent blind spots of fixed cameras, resolving inefficient exploration. Experimental results on the HM3D dataset demonstrate that SurveilNav substantially outperforms existing methods, achieving state-of-the-art performance in both exploration efficiency and navigation success rate. Moreover, the system shows strong potential for applications in large-scale search, home environments, and rescue missions.
3D Gaussian Splatting (3DGS) has garnered significant attention in Simultaneous Localization and Mapping (SLAM) due to its advances in capturing fine-grained geometry features and synthesizing novel views. For SLAM in large-scale scenes, such as autonomous driving, 3DGS-SLAM faces a critical limitation: memory consumption increases continuously over time as Gaussian points accumulate, leading to poor memory efficiency and limiting its applicability. In this work, we propose a rendering-area-aware pruning strategy that selectively removes Gaussians based on their contribution to the effective rendering area, rather than solely relying on Gaussian-level heuristics such as opacity or gradient magnitude. This perspective directly targets the sources of memory redundancy, effectively reducing the peak memory footprint of 3DGS-SLAM during runtime. Evaluations on the EuRoC and KITTI datasets demonstrate that our method consistently outperforms existing pruning approaches in large-scale outdoor scenes, achieving over 60% memory reduction and more than 2 times FPS improvement while preserving localization and mapping accuracy. These results highlight rendering-area-aware pruning as a promising direction for scaling 3DGS-SLAM to real-world autonomous driving scenarios. Our code is publicly available at https://github.com/UMN-ZhaoLab/Pocket-SLAM.git.
Deploying robots in unstructured real-world environments needs accurate, interactive models of the objects. Constructing these models at scale remains a critical bottleneck for robotic system integration. We present ArtiTwinSplat, a framework that automatically constructs articulated, photo-realistic digital twins of objects directly from RGB-D videos, requiring no CAD models, simulation assets, or manual annotations. Our method is built on 3D Gaussian Splatting that preserve geometric fidelity and photometric realism, coupled with an unsupervised articulation discovery pipeline that recovers part structure and joint kinematics from observed motion alone. With tracking and optimization stages our method provides stable, queryable digital twins that support real-time rendering, viewpoint control, and interactive manipulation. Unlike prior methods confined to simulation, ArtiTwinSplat operates directly on real-world observations and produces twins that are immediately usable by downstream robot planning and learning systems. This method offers a practical, scalable pathway toward digital twin construction, lowering the integration barrier for articulated object manipulation in embodied AI and human-robot collaboration contexts.
Modern autonomous Cyber-Physical Systems (CPSs), such as self-driving cars, face increasingly complex demands, and yet are expected to act reliably. The black-box nature often characterizing such systems, especially those relying on neural components, makes it impossible to fully verify the system behavior prior to deployment. Unfortunately, unexpected failures-when the system does not comply with its specification-are inevitable and may have catastrophic implications. To improve trust in the system and facilitate future mitigation after a failure occurs, it is important to try to derive an explanation for the unexpected system behavior. This paper introduces the novel concept of leveraging the framework of actual causality for CPS failure explanation. Up until now, this framework was only used to derive explanations in the context of simple systems, such as image classifiers. This paper addresses the theoretical gaps and provides the guidance needed to allow for correct explanation derivation in the CPS domain. Beyond the theoretical contribution, the paper presents two novel, practical, system-agnostic explanation derivation algorithms, allowing to prioritize either explanation optimality or derivation efficiency. The approach is demonstrated and evaluated in the context of a neural-network-controlled autonomous car, designed to avoid collisions.
Diffusion policies enable multimodal robot behavior but offer limited ability to choose among behavior modes at inference time, even though such control is desirable in human-robot settings. Prior solutions to this lack of control have utilized Signal Temporal Logic (STL) to express human intentions and provide corresponding guidance for diffusion policy inference. However, these approaches can only guide diffusion policies that jointly generate future actions and states, increasing both complexity and runtime. We propose a novel guidance method for action-only diffusion policies that uses a separate learned world model to enable differentiable evaluation of STL robustness, with its gradient then injected into the diffusion process. This steers behavior toward constraint satisfaction without retraining, improving constraint adherence while preserving task performance. On the Can Transport task from Robomimic, our method maintains 100% task success while reducing constraint violations from over 80% for baseline methods to 4%. We also discuss extensions toward improved robustness and more complex constraints.
In this report, we present our submission to the GOOSE 2D Fine-Grained Semantic Segmentation Challenge, organized as part of the Workshop on Field Robotics at ICRA 2026. The challenge combines data from the GOOSE and GOOSE-Ex datasets, which comprise more than 13k images captured from 4 distinct camera setups, annotated using a hierarchical taxonomy of 56 fine-grained classes and 11 broader categories. Starting from SegFormer as a baseline, we progressively improve segmentation performance through increased training crop sizes, a transition to the query-based Mask2Former architecture, and test-time augmentation. Our experiments show that query-based segmentation significantly outperforms the baseline model. Furthermore, increasing the crop size used during training yields substantial gains, highlighting the relevance of preserving scene context for fine-grained semantic disambiguation. Our final submission, using test-time augmentation, achieves an mIoU of 69.6% on the challenge test set, providing a strong baseline for fine-grained semantic segmentation in outdoor environments. To facilitate reproducibility and future research, code and weights will be made publicly available at https://github.com/RoboticsLabURJC/outdoor-fine-grained-segmentation .
Robot-Assisted Surgery is integral to modern minimally invasive procedures, with automation emerging as the next frontier to enhance precision and reduce surgeon fatigue. This evolution is largely impeded by the inherent kinematic inaccuracies of surgical robots, where unreliable internal sensors lead to significant control errors. While previous methods attempted to mitigate these issues through complex model-based calibration, they often suffer from high cost and limited effectiveness. This work utilises a learning-policy to actively compensate for hardware inaccuracies using closed-loop visual feedback that was trained from a teacher-student learning framework. The policy can fuse unreliable internal readings with precise external visual data, allowing it to correct for kinematic errors in real time without needing a perfect physical model. The learned policy was successfully deployed on the da Vinci Research Kit, where experiments validated the fundamental feasibility of using external vision to overcome internal sensor deficits. This research provides a foundational and reliable control methodology, paving the way for more advanced and robust surgical automation.
3D Gaussian Splatting (3DGS) has significantly boosted novel view synthesis and high-fidelity scene reconstruction, expanding the potential of 3DGS-based Visual Simultaneous Localization and Mapping (SLAM) methods. However, most existing systems fail to fully exploit the underlying structural information, which limits rendering quality and often leads to inconsistent maps. To address these limitations, we propose MMD-SLAM, a structure-enhanced Visual SLAM framework that leverages the Atlanta World (AW) assumption to guide a Multi-Meta Gaussian representation for photorealistic mapping. First, we introduce a point-line fusion strategy for pose optimization, where 3D line segments are incorporated to improve tracking robustness and provide additional constraints for mapping. Second, we design a Multi-Meta Gaussian representation with dominant directions, explicitly encoding structural priors from the AW hypothesis. Finally, we propose a Gaussian evolution strategy that adapts to scene geometry and incorporates structural cues into global optimization. Extensive experiments demonstrate that these innovations enable MMD-SLAM to achieve state-of-the-art performance in both tracking accuracy and mapping quality. e.g., our method achieves a 48.56% reduction in ATE RMSE on ScanNet and a 5.71% improvement in PSNR on Replica, compared with MonoGS.
To address cumulative localization drift of unmanned ground vehicles in structured road environments under severe Global Navigation Satellite System signal occlusion, this paper proposes a robust route-constrained state estimation method. During periods without satellite signals, the proposed method establishes the correspondence between the historical dead reckoning trajectory and local segments of the mission route extracted from a high-definition map, and estimates a route-referenced position via a two-dimensional rigid transformation. The estimated position is then formulated as a pseudo-position observation and incorporated into an Extended Kalman Filter update. In this way, route constraints at the road level can be continuously injected into a unified state estimation framework, thereby suppressing position deviation relative to the mission route while indirectly improving azimuth estimation. To enhance practical applicability, engineering strategies, such as trigger control, matching quality validation, route offset compensation, and single update correction limiting, are further introduced. Experiments in three representative scenarios, including a long tunnel, a multi-segment tunnel, and a curved tunnel, show that the proposed method effectively suppresses error accumulation during satellite outages, reduces the risk of large maximum deviation, and improves localization continuity and road-level usability.
Autonomous Emergency Braking (AEB) optimization relies on accurately annotated real-world trigger events, particularly rare but critical delayed and false AEB triggers that expose system deficiencies. However, these minority samples comprise less than 5% of thousands of daily triggers, making manual annotation prohibitively expensive at scale. We present the first automated AEB annotation framework to address this problem. During development, we identified two fundamental challenges that severely impair delayed/false trigger annotation accuracy: (1) Extreme class imbalance where delayed/false triggers are overwhelmed by true triggers; (2) Asymmetric label noise where mislabeled majority samples (true triggers) suppress minority samples (delayed/false triggers) learning. To overcome these challenges, we propose two key innovations: (1) Specific data augmentation that synthesizes realistic samples by manipulating focal target attributes, transplanting ego-vehicle dynamics, and masking non-focal agents; (2) noise suppression using stable hardness estimation and probe-guided adaptive threshold to clean mislabeled true trigger samples. Crucially, we deploy our model as a practical annotation system with full-stack architecture, efficiently identifying critical delayed/false triggers from thousands of daily AEB events. Production results demonstrate 80% improvement in recall of delayed/false triggers and 50% reduction in manual workload. Beyond immediate gains, the system enables continuous self-improvement through accumulated high-quality annotations, establishing a necessary data foundation for on-vehicle AEB system optimization
The autonomous localization of fugitive gas emissions using small Unmanned Aircraft Systems (sUAS) constitutes a fundamentally ill-posed inverse problem. In turbulent atmospheric boundary layers, highly intermittent scalar concentration fields violate the assumptions of classical gradient-based navigation, causing data-driven estimators to suffer from severe noise and spurious local minima. To address these challenges, we introduce an Information-Guided Safe Reinforcement Learning framework evaluated within a custom, GPU-accelerated 3D simulation environment coupling an Eulerian wind solver with a Lagrangian puff dispersion model. We identify a critical vulnerability in deterministic information-seeking planners - a Gramian bias where agents act greedily upon flawed early estimates, starving the estimator of spatial diversity. To systematically break this degeneracy, our architecture integrates a classical empirical observability Gramian (EMGR) planner with a learned Soft Actor-Critic (SAC) exploratory policy. A deterministic meta-supervisor actively monitors estimator reliability via Kullback-Leibler (KL) divergence, dynamically blending deterministic exploitation with learned exploration to steer the sUAS into high-information zones. Trained via a progressive curriculum and safeguarded by a strictly enforced Robust Control Barrier Function (RCBF), our RL framework achieves nearly 80% localization success on complex, mobile sources - drastically outperforming classical baselines (~30%) - while ensuring zero safety violations.
This paper presents a control barrier function-based method for real-time in-domain congestion control of the Lighthill-Whitham-Richards traffic model. Traffic congestion is formulated as a distributed safety control problem, leading to a infinite-dimensional optimization problem. Through the discretization and Karush-Kuhn-Tucker (KKT) analysis, the problem is converted into a high-dimensional quadratic program. A structure-exploiting primal-dual active set algorithm is then developed to compute the safe control input in real time, with convergence guarantees. Numerical simulations with different nominal controllers demonstrate the effectiveness and real-time feasibility of the proposed approach.
Quadratic programs (QPs) using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are widely used for safe control in reach-and-avoid navigation. However, the inherently conflicting nature of CBF and CLF constraints can lead to performance degradation, including slowdowns and deadlocks. This issue is exacerbated in multi-goal scenarios, where multiple nominal control objectives must be satisfied under shared safety constraints. Existing approaches for preemptive safety are often computationally expensive or overly conservative, while methods that relax or switch between nominal objectives are not well-suited for sequential goal-to-goal navigation. To address these limitations, we propose a conflict-aware switching strategy that detects high-conflict conditions and switches between available nominal control objectives to reduce constraint conflict. We apply this approach to multi-agent, multi-goal reach-and-avoid scenarios under CBF-CLF-QP control. Compared to a baseline sequential goal traversal strategy, our method reduces both completion time and timeout rates, demonstrating improved performance in satisfying all nominal control objectives while respecting safety constraints.
Safe navigation for an ego vehicle in uncertain environments characterized by dynamic obstacles with unknown nonlinear dynamics is a challenging problem of significant practical interest. Existing approaches in the literature either lack formal safety guarantees, require full model knowledge, or fail to account for the risk associated with the vehicle's exact body geometry and the temporal evolution of uncertainty between sampling instants. In this paper, we propose a data-driven observer for the unknown obstacle dynamics that generates an alpha-confidence set flow, which is exactly transformed into a Control Barrier Function (CBF) to enforce (1-alpha)-probability safety. The proposed framework accommodates nonlinear ego vehicle dynamics of arbitrary relative degree, as demonstrated through case studies involving first- and second-order dynamics of an unmanned surface vehicle.
Safety-critical control systems, such as spacecraft performing proximity operations, must provide formal safety guarantees despite stochastic uncertainties from state estimation and unmodeled dynamics. Although Control Barrier Functions (CBFs) have been extended to stochastic systems, existing approaches typically face a trade-off between the tightness of probabilistic guarantees and computational tractability. This paper presents a particle-based probabilistic CBF framework that overcomes this limitation by exploiting the sub-Gaussian structure of the barrier function increment under Gaussian uncertainties. We establish that Gaussian uncertainties propagating through Lipschitz-continuous control-affine dynamics preserve sub-Gaussianity of the barrier function increment, with explicit tail bounds. Leveraging this structure, we derive finite-sample bounds on the approximation error between particle-based Conditional Value at Risk (CVaR) estimates and ground-truth probabilistic constraints; applying this yields a tractable optimization problem formulation with finite-sample safety certificates. We show through numerical experiments how the proposed approach provides tight yet provably valid probabilistic safety guarantees.
Control barrier functions (CBFs) provide a principled framework for enforcing safety in control systems -- yet the certified safe operating region in practice is often conservative, especially under input bounds. In many applications, multiple smaller safe sets can be certified independently, e.g., around distinct equilibria with different stabilizing controllers. This paper proposes a framework for uniting such regions into a single certified safe set using \emph{combinatorial CBFs}. We refine the combinatorial CBF framework by introducing an auxiliary variable that enables logical compositions of individual CBFs. In the proposed framework, we show that such compositions yield a \emph{generalized combinatorial CBF} under a condition termed \emph{conjunctive compatibility}. Building on this result, we extend the framework to enable the aggregation of multiple implicit safe sets generated by the backup CBF framework. We show that the resulting CBF-based quadratic program yields a continuous safety filter over the aggregated safe region. The approach is demonstrated on two spacecraft safety problems, safe attitude control and safe station keeping, where multiple certified safe regions are combined to expand the operational envelope.
A tube-based safety framework is presented for robust anticipative tracking in nonlinear Brunovsky multi-agent systems subject to bounded disturbances. The architecture establishes robust safety certificates for a feedforward-augmented ancillary control policy. By rendering the state-deviation dynamics independent of the agents' internal nonlinearities, the formulation strictly circumvents the restrictive Lipschitz-bound feasibility conditions otherwise required for robust stabilization. Consequently, this structure admits an explicit, closed-form robust positively invariant (RPI) tube radius that systematically attenuates the exponential control barrier function (eCBF) tightening margins, thereby mitigating constraint conservatism while preserving formal forward invariance. Within the distributed model predictive control (MPC) layer, mapping the local tube radii through the communication graph yields a closed-form global formation error bound formulated via the minimum singular value of the augmented Laplacian. Robust inter-agent safety is enforced with minimal communication overhead, requiring only a single scalar broadcast per neighbor at initialization. Numerical simulations confirm the framework's efficacy in safely navigating heterogeneous formations through cluttered environments.
Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-conservative safety guarantees due to significant relaxation gaps. While the completely positive program (CPP) formulation closes this gap, it is NP-hard to solve. Its cheapest tractable relaxation, the doubly non-negative program (DNN), retains critical constraints as an SDP, but one whose size exceeds the reach of interior-point methods at practical scale. While Burer-Monteiro (BM) factorization has been applied to make SDP-based verification scalable, no such result exists for the strictly tighter DNN formulation. A key obstacle is that additional non-negativity constraints in the DNN cause dual multipliers for optimality certification to be non-unique, making standard certification methods inapplicable. We propose a novel eigenvalue maximization procedure that searches the non-unique multiplier space for a valid certificate, i.e. a global optimality guarantee. Experiments demonstrate that our approach $(\text{DNN})^2$ produces bounds consistently tighter than the standard SDP method, often matching the exact solution, and that our certification procedure confirms global optimality when a valid certificate exists. These results are a key step toward providing tight, certifiable, and computationally scalable verification guarantees needed to deploy neural network controllers and perception modules in safety-critical autonomous systems.
We study bilateral teleoperation between nonlinear, multi-DOF robotic manipulators in the presence of constant communication delays. Unlike classical wave-transformation architectures that transmit a coordinating force, we consider the case where the environmental force is reflected to the master side to enhance teleoperation transparency. Since direct contact force feedback might destabilize the closed-loop system, we first develop a passivity-shortage characterization for the Euler--Lagrange remote system using a linear matrix inequality (LMI) approach. An upper strictly passive communication law is then employed to compensate for the computed passivity shortage so that the closed-loop stability under delays as well as position and force synchronization are preserved under appropriate conditions. Simulations with nonlinear 2-DOF robotic manipulators in different settings illustrate our approach.
This paper proposes a controller design method for shaping the controllability Gramian into a desired form to design the effect from exogenous inputs to the system state. Using the Bures--Wasserstein distance, we formulate the shaping problem as the minimization of the distance between the system Gramian and a desired Gramian, and the objective function is shown to be strictly convex on the set of symmetric positive definite matrices. In addition, by deriving a semidefinite programming formulation via a linear matrix inequality (LMI), computational efficiency is improved and additional LMI constraints can be incorporated. When the exogenous input is modeled as Gaussian white noise, the proposed framework is closely related to $H_2$ control, which can be interpreted as a special case of optimal transport. Numerical examples demonstrate anisotropic controllability design for a guidance robot and verify the ability to impose additional directional constraints through LMIs. The numerical examples also confirm that the proposed method approaches $H_2$ control as the desired Gramian tends to zero.
Shared autonomy requires principled mechanisms for allocating and transferring control between a human and an autonomous agent. Existing approaches often rely on blending control inputs or heuristic switching rules, which lack theoretical guarantees and fail to account for the dynamics of authority transfer. This paper develops a cooperative game-theoretic framework for authority switching in shared autonomy. We formulate the control switching problem as an identical-interest dynamic game in which authority transitions are embedded into the system dynamics, yielding optimal switching policies rather than ad hoc rules. We establish the existence and characterization of team-optimal policies in pure strategies under stochastic human override, accounting for asymmetric authority where humans retain override capability. For linear-quadratic systems, we derive closed-form recursions for the optimal switching policies and value functions, enabling efficient computation independent of the continuous state. We validate the framework on scalar and multi-dimensional linear systems, demonstrating how optimal switching adapts to varying system dynamics, cost structures, and override probabilities. The results reveal fundamental trade-offs between human adaptability and autonomous efficiency, illustrating the practical benefits of grounding shared autonomy in cooperative game theory.
This paper addresses multi-objective kinodynamic planning in environments with stochastic hybrid adversaries that probabilistically transition to adversarial modes based on the ego state. The goal is to construct the Pareto-front of paths that trade off execution cost and the probability of safety constraint violation (risk). Existing chance-constrained planners evaluate risk over open-loop trajectories, yielding overly conservative solutions that fail to account for ego-agent reactivity. To address this limitation, we shift the planning space to sequences of closed-loop policies, and integrate sample-based risk evaluation directly into tree construction via Monte-Carlo particle rollouts. We first introduce Stochastic Multi-Objective RRT (SMO-RRT), for which we prove probabilistic completeness, followed by Stochastic Multi-Objective Stable Sparse RRT (SMO-SST), which leverages selective pruning to improve numerical performance at the cost of completeness. For both algorithms, we derive a finite-sample bound on the probability of chance constraint violation for systems with non-Gaussian, state-dependent uncertainty, enabling probabilistically safe planning in a broad class of environments applicable to multi-agent systems, social navigation, and autonomous driving.
Safely navigating polytopic environments while respecting the dynamics, control, and exact geometry of the underlying system is a challenge in robotics. Control barrier functions (CBFs) synthesize safe control policies by rendering the safe set forward invariant, but many existing CBF-based methods approximate polytopes using conservative smooth shapes, such as spheres or ellipsoids, to obtain explicit differentiable distance functions. In this article, we propose an exact Signed Distance Function (SDF) formulation for a {\it polytopic} robot and {\it polytopic} obstacles and integrate it with nonsmooth CBFs. Leveraging Minkowski operations, the proposed method computes the exact SDF via companion convex programs in both the collision-free (positive-sign) and in-collision (negative-sign) cases. Furthermore, by exploiting the convenient geometric properties of 2D Minkowski operations and the optimality conditions of the two companion convex programs, we derive a unified analytical expression for the gradient of the exact SDF via sensitivity analysis. The exact rotational gradient further reveals a previously masked class of local minima induced by the coupling between geometry and nonholonomic kinematics. We demonstrate the effectiveness of the proposed framework through a pure-translation case and three scenarios with unicycle models involving recovery from an unsafe initialization and single- and multiple-obstacle avoidance. Comparisons with baseline methods highlight how the proposed framework enables non-conservative maneuvers and safety recovery.
Control Barrier Functions (CBFs) have emerged as efficient tools to address the safe navigation problem for robot applications. However, synthesizing informative and obstacle motion-aware CBFs online using real-time sensor data remains challenging, particularly in unknown and dynamic scenarios. Motived by this challenge, this paper aims to propose a novel Gaussian Process-based formulation of CBF, termed the Dynamic Log Gaussian Process Control Barrier Function (DLGP-CBF), to enable real-time construction of CBF which are both spatially informative and responsive to obstacle motion. Firstly, the DLGP-CBF leverages a logarithmic transformation of GP regression to generate smooth and informative barrier values and gradients, even in sparse-data regions. Secondly, by explicitly modeling the DLGP-CBF as a function of obstacle positions, the derived safety constraint integrates predicted obstacle velocities, allowing the controller to proactively respond to dynamic obstacles' motion. Simulation results demonstrate significant improvements in obstacle avoidance performance, including increased safety margins, smoother trajectories, and enhanced responsiveness compared to baseline methods.
In this paper we address the problem of control Lyapunov-barrier function (CLBF)-based safe stabilization for a class of nonlinear control-affine systems. A difficulty may arise for the case when a constraint has the relative degree larger than 1, at which computing a proper CLBF is not straightforward. Instead of adding an (possibly non-existent) control barrier function (CBF) to a control Lyapunov function (CLF), our key idea is to simply scale the value of the CLF on the unsafe set, by utilizing a sigmoid function as a scaling factor. We provide a systematic design method for the CLBF, with a detailed condition for the parameters of the sigmoid function to satisfy. It is also seen that the proposed approach to the CLBF design can be applied to the problem of task-space control for a planar robot manipulator with guaranteed safety, for which a safe feedback linearization-based controller is presented.
Control barrier functions (CBFs) are a powerful tool for the constrained control of nonlinear systems; however, the majority of results in the literature focus on systems subject to a single CBF constraint, making it challenging to synthesize provably safe controllers that handle multiple state constraints. This paper presents a framework for constrained control of nonlinear systems subject to box constraints on the systems' vector-valued outputs using multiple CBFs. Our results illustrate that when the output has a vector relative degree, the CBF constraints encoding these box constraints are compatible, and the resulting optimization-based controller is locally Lipschitz continuous and admits a closed-form expression. Additional results are presented to characterize the degradation of nominal tracking objectives in the presence of safety constraints. Simulations of a planar quadrotor are presented to demonstrate the efficacy of the proposed framework.
Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems. Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets. However, computing CBFs generally involves addressing a complex robust optimization problem, which can be intractable. Scenario-based methods have been proposed to simplify this computation. Then, one needs to verify if the CBF actually satisfies the robust constraints. We present an approach to perform this verification that relies on Lipschitz arguments, and forms the basis of a certification algorithm designed for sample efficiency. Through a numerical example, we validated the efficiency of the proposed procedure.
We consider the problem of adaptively monitoring a wildfire front using a mobile agent (e.g., a drone), whose trajectory determines where sensor data is collected and thus influences the accuracy of fire propagation estimation. This is a challenging problem, as the stochastic nature of wildfire evolution requires the seamless integration of sensing, estimation, and control, often treated separately in existing methods. State-of-the-art methods either impose linear-Gaussian assumptions to establish optimality or rely on approximations and heuristics, often without providing explicit performance guarantees. To address these limitations, we formulate the fire front monitoring task as a stochastic optimal control problem that integrates sensing, estimation, and control. We derive an optimal recursive Bayesian estimator for a class of stochastic nonlinear elliptical-growth fire front models. Subsequently, we transform the resulting nonlinear stochastic control problem into a finite-horizon Markov decision process and design an information-seeking predictive control law obtained via a lower confidence bound-based adaptive search algorithm with asymptotic convergence to the optimal policy.
This article proposes a nonlinear microscopic dynamical model for autonomous electric vehicles (A-EVs) that considers battery energy efficiency in the car-following dynamics. The model builds upon the Optimal Velocity Model (OVM), with the control term based on the battery dynamics to enable thermally optimal and energy-efficient driving. We rigorously prove that the proposed model achieves lower energy consumption compared to the Optimal Velocity Follow-the-Leader (OVFL) model. Through numerical simulations, we validate the analytical results on the energy efficiency. We additionally investigate the stability properties of the proposed model.
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data generated by solving a sample of infinite- dimensional optimization problems using composite Bernstein collocation. Once trained, the Transformer efficiently generates near-optimal, feasible trajectories, making it well-suited for real-time applications. In motion planning for autonomous vehicles, for instance, these trajectories can serve to warm- start optimal motion planners or undergo rigorous evaluation to ensure safety. We demonstrate the effectiveness of this method through numerical results on a classical control problem and an online obstacle avoidance task. This data-driven approach offers a promising solution for real-time optimal control of nonlinear, nonconvex systems.
Ellipsoidal tube-based model predictive control methods effectively account for the propagation of the reachable set, typically employing linear feedback policies. In contrast, scenario-based approaches offer more flexibility in the feedback structure by considering different control actions for different branches of a scenario tree. However, they face challenges in ensuring rigorous guarantees. This work aims to integrate the strengths of both methodologies by enhancing ellipsoidal tube-based MPC with a scenario tree formulation. The uncertainty ellipsoids are partitioned by halfspaces such that each partitioned set can be controlled independently. The proposed ellipsoidal multi-stage approach is demonstrated in a human-robot system, highlighting its advantages in handling uncertainty while maintaining computational tractability.
Mean Field Games (MFGs) offer a powerful framework for studying large-scale multi-agent systems. Yet, learning Nash equilibria in MFGs remains a challenging problem, particularly when the initial distribution is unknown or when the population is subject to common noise. In this paper, we introduce an efficient deep reinforcement learning (DRL) algorithm designed to achieve population-dependent Nash equilibria without relying on averaging or historical sampling, inspired by Munchausen RL and Online Mirror Descent. The resulting policy is adaptable to various initial distributions and sources of common noise. Through numerical experiments on seven canonical examples, we demonstrate that our algorithm exhibits superior convergence properties compared to state-of-the-art algorithms, particularly a DRL version of Fictitious Play for population-dependent policies. The performance in the presence of common noise underscores the robustness and adaptability of our approach.
This paper develops a certified constraint-reduction method for distributed model predictive control with tube-tightened exponential control barrier functions (eCBFs) in multi-agent systems. At each prediction stage, pairwise agent--agent and agent--obstacle eCBF conditions define halfspaces in the local control space. Rather than enforcing all such halfspaces, a geometry-adaptive subset is retained and a Farkas certificate verifies that the reduced admissible set is contained in the full tightened set. For planar inputs, cone coverage is characterized through the largest angular gap: two extreme directions suffice in the strict half-plane regime, while other geometries initialize with three retained constraints and escalate only when certification fails. Conic multipliers and nominal-aware offsets are obtained in closed form, without an auxiliary optimization, and the resulting construction preserves any nominal control already admissible for the full tightened set. Consequently, the reduced controller inherits the robust safety guarantee of the underlying tube-eCBF formulation. In a ten-follower, four-obstacle study, the method retained fewer safety constraints on average, reproduced the full filter's nominal accept/reject decisions with no true safety violations, and achieved increasing computational gains as the constraint count and prediction horizon grew.
Control Barrier Functions (CBFs) have been proposed to ensure safety of autonomous systems. This paper considers control policies that switch between CBF constraints. Under this approach, we represent a complex non-convex safe region as a union of sets that are computationally tractable to verify. We denote this framework as union-CBFs and make the following contributions. First, considering switching CBF-QP controllers, we propose a sufficient condition that ensures (i) the system undergoes a finite number of switches in any finite time interval and ensures (ii) the forward invariance of the closed-loop system in between switches. Second, we consider two types of switching strategies and propose union-CBFs conditions for each strategy to satisfy (i) and (ii). Third, we formulate Sum-of-Squares (SOS) algorithms to verify the conditions. The experiments show that our union-CBFs framework results in a larger safe region compared to high-degree polynomial CBFs. We also show the efficiency of the verification algorithms using a polynomial system model.
This paper presents a novel framework for ensuring safety in dynamically coupled multi-agent systems through collaborative control. Drawing inspiration from ecological models of altruism, we develop collaborative control barrier functions that allow agents to cooperatively enforce individual safety constraints under coupling dynamics. We introduce an altruistic safety condition based on the so-called Hamilton's rule, enabling agents to trade off their own safety to support higher-priority neighbors. By incorporating these conditions into a distributed optimization framework, we demonstrate increased feasibility and robustness in maintaining system-wide safety. The effectiveness of the proposed approach is illustrated through simulation in a simplified formation control scenario.
Reinforcement Learning (RL) has shown promise in various robotics applications, yet its deployment on real systems is still limited due to safety and operational constraints. The safe RL field has gained considerable attention in recent years, which focuses on imposing safety constraints throughout the learning process. However, real systems often require more complex constraints than just safety, such as periodic recharging or time-bounded visits to specific regions. Imposing such spatio-temporal tasks during learning still remains a challenge. Signal Temporal Logic (STL) is a formal language for specifying temporal properties of real-valued signals and provides a way to express such complex tasks. In this paper, we propose a framework that leverages sequential control barrier functions and model-free RL to ensure that the given STL tasks are satisfied throughout the learning process. Our method extends beyond traditional safety constraints by enforcing rich STL specifications, which can involve visits to dynamic targets with unknown trajectories. We also demonstrate the effectiveness of our framework through various simulations.
The ability to manipulate and interlace cables using aerial vehicles can greatly improve aerial transportation tasks. Such interlacing cables create hitches by winding two or more cables around each other, which can enclose payloads or can further develop into knots. Dynamic modeling and control of such hitches are key to mastering inter-cable interactions in the context of cable-suspended aerial manipulation. This paper introduces an ellipsoid-based kinematic model to connect the geometric nature of a hitch created by two cables and the dynamics of the hitch driven by four aerial vehicles, which reveals the control-affine form of the system. As the constraint for maintaining tension of a cable is also control-affine, we design a quadratic programming-based controller that combines Control Lyapunov and High-Order Control Barrier Functions (CLF-HOCBF-QP) to precisely track a desired hitch position and system shape while enforcing safety constraints like cable tautness. We convert desired geometric reference configurations into target robot positions and introduce a composite error into the Lyapunov function to ensure a relative degree of one to the input. Numerical simulations validate our approach, demonstrating stable, high-speed tracking of dynamic references.
This paper studies the safe control of very large multi-agent systems via a generalized framework that employs so-called Banach Control Barrier Functions (B-CBFs). Modeling a large swarm as probability distribution over a spatial domain, we show how B-CBFs can be used to appropriately capture a variety of macroscopic constraints that can integrate with large-scale swarm objectives. Leveraging this framework, we define stable and filtered gradient flows for large swarms, paying special attention to optimal transport algorithms. Further, we show how to derive agent-level, microscopical algorithms that are consistent with macroscopic counterparts in the large-scale limit. We then identify conditions for which a group of agents can compute a distributed solution that only requires local information from other agents within a communication range. Finally, we showcase the theoretical results over swarm systems in the simulations section.
This paper investigates bounds on the estimation error of a linear system affected by norm-bounded disturbances and full sensor attacks. The system is equipped with a detector that evaluates the norm of the innovation signal to detect faults, and the attacker wants to avoid detection. We utilize induced $L_\infty$ system norms, also called \emph{peak-to-peak} norms, to compare the estimation error bounds under nominal operations and under attack. This leads to a sufficient condition for when the bound on the estimation error is smaller during an attack than during nominal operation. This condition is independent of the attack strategy and depends only on the attacker's desire to remain undetected and (indirectly) the observer gain. Therefore, we investigate both an observer design method, that seeks to reduce the error bound under attack while keeping the nominal error bound low, and detector threshold tuning. As a numerical illustration, we show how a sensor attack can deactivate a robust safety filter based on control barrier functions if the attacked error bound is larger than the nominal one. We also statistically evaluate our observer design method and the effect of the detector threshold.
We present a robust safety-critical control framework tailored for networked susceptible-infected-recovered (SIR) epidemic dynamics, leveraging control barrier functions (CBFs) and robust control barrier functions to address the challenges of epidemic spread and mitigation. In our networked SIR model, each node must keep its infection level below a critical threshold, despite dynamic interactions with neighboring nodes and inherent uncertainties in the epidemic parameters and measurement errors, to ensure public health safety. We first derive a CBF-based controller that guarantees infection thresholds are not exceeded in the nominal case. We enhance the framework to handle realistic epidemic scenarios under uncertainties by incorporating compensation terms that reinforce safety against uncertainties: an independent method with constant bounds for uniform uncertainty, and a novel approach that scales with the state to capture increased relative noise in early or suppressed outbreak stages. Simulation results on a networked SIR system illustrate that the nominal CBF controller maintains safety under low uncertainty, while the robust approaches provide formal safety guarantees under higher uncertainties; in particular, the novel method employs more conservative control efforts to provide larger safety margins, whereas the independent approach optimizes resource allocation by allowing infection levels to approach the boundaries in steady epidemic regimes.
Control barrier functions (CBFs) have a well-established theory in Euclidean spaces, yet still lack general formulations and constructive synthesis tools for systems evolving on manifolds common in robotics and aerospace applications. In this paper, we develop a general theory of geometric CBFs on bundles and, for control-affine systems, recover the standard optimization-based CBF controllers and their smooth analogues. Then, by generalizing kinetic energy-based CBF backstepping to Riemannian manifolds, we provide a constructive CBF synthesis technique for geometric mechanical systems, as well as easily verifiable conditions under which it succeeds. Further, this technique utilizes mechanical structure to avoid computations on higher-order tangent bundles. We demonstrate its application to an underactuated satellite on SO(3).
Safety-critical control is imperative for deploying autonomous systems in the real world. Control Barrier Functions (CBFs) offer strong safety guarantees when accurate system and sensor models are available. However, widely used additive, fixed-noise models are not representative of complex sensor modalities with state-dependent error characteristics. Although CBFs have been designed to mitigate uncertainty using fixed worst-case bounds on measurement noise, this approach can lead to overly-conservative control. To solve this problem, we extend the Belief Control Barrier Function (BCBF) framework to accommodate state-dependent measurement noise via the Generalized Extended Kalman Filter (GEKF) algorithm, which models measurement noise as a linear function of the state. Using the original BCBF framework as baseline, we demonstrate the performance of the BCBF-GEKF approach through simulation results on a 1D single integrator setpoint tracking scenario and 2D unicycle kinematics trajectory tracking scenario. Our results confirm that the BCBF-GEKF approach offers less conservative control with greater safety.
This paper presents a decentralized safety filter for collision avoidance in multi-agent aerospace interception scenarios. The approach leverages robust control barrier functions (RCBFs) to guarantee forward invariance of safe sets under bounded inputs and high-relative-degree dynamics. Each effector executes its nominal cooperative guidance command, while a local quadratic program (QP) modifies the input only when necessary. Event-triggered activation based on range and zero-effort miss (ZEM) criteria ensures scalability by restricting active constraints to relevant neighbors. To ensure feasibility under multiple simultaneously active constraints, a slack-variable relaxation scheme is introduced that prioritizes critical agents in a Pareto-optimal manner. Simulation results in many-on-many interception scenarios demonstrate that the proposed framework maintains collision-free operation with minimal deviation from nominal guidance, providing a computationally efficient and scalable solution for safety-critical multi-agent aerospace systems.
Soft landing on small celestial bodies (SCBs) poses unique challenges, as gravitational models poorly characterize the higher-order gravitational effects of SCBs. Existing control approaches lack guarantees for safety under gravitational uncertainty. This paper proposes a three-stage control architecture that combines disturbance estimation, trajectory tracking, and safety enforcement. An extended high-gain observer estimates gravitational disturbances online, a feedback-linearizing controller tracks a reference trajectory, and a minimum-intervention quadratic program enforces state and input constraints while remaining close to the nominal control. The proposed approach enables aggressive yet safe maneuvers despite gravitational uncertainty. Numerical simulations demonstrate the effectiveness of the controller in achieving soft-landing on irregularly shaped SCBs, highlighting its potential for autonomous SCB missions.
Recent machine learning research has increasingly focused on equilibrium analysis in non-cooperative games rather than solely on optimal solutions. Many such problems involve shared constraints and can be formulated as Generalized Nash Equilibrium Problems (GNEPs). For strongly monotone games, existing methods compute consensus-based variational GNEs (v-GNEs) by exchanging Lagrange multipliers. We propose a fully distributed continuous-time algorithm for shared linear equality constraints that converges without multiplier exchange and reaches any GNE, reducing communication overhead and improving privacy. Discrete-time schemes are also provided, and the method is validated on a multi-robot placement task.
Large-scale robotic swarms motivate the use of mean-field control (MFC). Classical partial differential equation (PDE)-based formulations provide a principled framework but can become computationally challenging in higher dimensions, whereas machine learning achieves scalability at the cost of approximation and guarantees. In this work, we establish an optimization-based framework that lifts the MFC problem into the space of occupation measures, resulting in a convex relaxation formulated as an optimization over measures. The resulting problem is solved using a Frank-Wolfe (FW) algorithm in the measure space, with each iteration reduced to a tractable optimal control problem. This approach retains the O(1/k) convergence rate of FW, avoids discretization of the state space, and naturally incorporates interaction and safety constraints. Numerical experiments demonstrate agreement with analytic and PDE-based baselines in two dimensions and show that the method scales to three-dimensional environments with multiple obstacles, where standard grid-based PDE solvers become impractical. A full 3D instance with ten obstacles is solved in minutes on a standard workstation, underscoring the practicality and scalability of the proposed framework.
In environmental monitoring as well as emergency response applications such as wildfires, wind velocity measurement is essential. Quadrotor UAVs have become popular platforms for wind velocity estimation due to their maneuverability, compact size, and cost-effectiveness. Numerous studies use the Extended Kalman Filter (EKF) to estimate the wind velocity based on the quadrotor dynamic model. However, most of them use hovering quadrotors only for wind estimation, others use a near-linear trajectory to estimate near-constant velocities. Furthermore, EKF performance is constrained by its reliance on linearized approximations of the nonlinear quadrotor dynamics around current states, limiting accuracy in highly nonlinear scenarios, including windy conditions. This study proposes the use of an Unscented Kalman Filter (UKF), a nonlinear estimator to provide accurate wind estimations while maintaining the trajectory of the quadrotor UAV. The quadrotor is modeled on the Special Euclidean group SE(3) and the approach is evaluated through numerical simulations using a geometric controller to maintain quadrotor flight paths. The results indicate that as the nonlinearity of the simulation increases, the UKF consistently outperforms the EKF. This demonstrates the potential of the UKF as a reliable estimator for highly nonlinear scenarios, capable of maintaining the trajectory with minimal deviation while providing accurate wind velocity estimations.
Connected and automated vehicle (CAV) platooning promises gains in energy efficiency and traffic throughput and, most critically, in safety. These safety benefits hinge on string stability, which determines how disturbances propagate along a platoon. While longitudinal string stability is well studied, lateral string stability, which governs the propagation of path-tracking errors that can lead to unsafe deviations from the intended path, remains underexplored. Its importance is increasing as autonomous vehicles rely more heavily on onboard sensing and map-free navigation, where sensor occlusion and dense formations amplify safety risks. This paper presents a new framework for lateral string stability that directly addresses safety-critical path-relative tracking errors and enables consistent comparison across vehicles following the same road geometry. Central to this framework is an arc-length (Eulerian) viewpoint, a departure from traditional analyses, that clarifies how tracking errors at a given point on the path propagate from one vehicle to the next. A formal definition of lateral string stability is introduced along with two control strategies: an onboard-sensing-only controller and a novel learn-from-predecessor approach utilizing vehicle-to-vehicle (V2V) communication. We show that onboard sensing alone cannot guarantee attenuation of path-tracking errors, imposing a fundamental safety limitation, whereas V2V communication enables true error attenuation.
Learning-based methods for synthesizing controllers have gained popularity due to their high expressiveness and strong empirical performance. However, in safety-critical scenarios such as autonomous driving, robotics, and power systems, empirical performance alone is insufficient, and formal verification of controller properties such as stability and safety is highly desirable. Unfortunately, many prior verification approaches are either tied to specific structural assumptions on the system or the certificate, making them difficult to transfer across settings, or suffer from poor scalability on higher-dimensional neural network systems. In this tutorial, we present a unified framework that aims to mitigate this gap via bridging control with the state-of-the-art neural network verifier $α,\!β$-CROWN (alpha-beta-CROWN). At its core, $α,\!β$-CROWN is a general-purpose bounding engine for nonlinear functions represented as computation graphs: given an input domain, it can produce certified bounds and explicit linear relaxation of the nonlinear function. These certified bounds are useful on their own for tasks such as reachability analysis, and they also provide the foundation for more complex routines that perform satisfiability checking and optimization. More specifically, many control problems reduce to verifying real-valued inequalities over a state domain (e.g., Lyapunov theory). Consequently, $α,\!β$-CROWN enables scalable verification of such conditions by computing tight bounds and recursively partitioning and pruning subdomains based on the bounds. Thanks to GPU parallelization, this pipeline demonstrates superior scalability on verification and optimization problems that are challenging for traditional approaches. In this tutorial, we discuss the basics of $α,\!β$-CROWN and introduce its application to various control-related tasks.
Remanufacturing is fundamentally more challenging than traditional manufacturing due to the significant uncertainty, variability, and incompleteness inherent in end-of-life (EoL) products. At the same time, it has become increasingly essential and urgent for facilitating a circular economy, driven by the growing volume of discarded electronic products and the escalating scarcity of critical materials. In this paper, we review the existing literature and examine the key challenges as well as emerging opportunities in intelligent automation for EoL electronics remanufacturing, providing a comprehensive overview of how robotics, control, and artificial intelligence (AI) can jointly enable scalable, safe, and intelligent remanufacturing systems. This paper starts with the definition, scope, and motivation of remanufacturing within the context of a circular economy, highlighting its societal and environmental significance. Then it delves into intelligent automation approaches for disassembly, inspection, sorting, and component reprocessing in this domain, covering advanced methods for multimodal perception, decision-making under uncertainty, flexible planning algorithms, and force-aware manipulation. The paper further reviews several emerging techniques, including large foundation models, human-in-the-loop integration, and digital twins that have the potential to support future research in this area. By integrating these topics, we aim to illustrate how next-generation remanufacturing systems can achieve robust, adaptable, and efficient operation in the face of complex real-world challenges.
Multi-drone payload transportation has emerged as a promising research paradigm with potential applications in construction, logistics, and disaster response. However, the complex coupled dynamics among drones, cables, and payloads pose significant challenges, and existing approaches remain limited in safety and scalability, particularly in dynamic and unstructured environments. In this work, we propose a learning-based framework for safe and scalable multi-drone cooperative payload transport. We introduce a minimal 2D abstraction that preserves the task-relevant drone-payload coupling required for coordination and safety, while remaining computationally efficient for large-scale learning. Using domain randomization over team size and physical parameters, we train a fully distributed policy via Discrete Graph Control Barrier Function Proximal Policy Optimization (DGPPO), enabling robust zero-shot sim-to-real transfer without fine-tuning. Extensive real-world evaluations demonstrate that a single learned policy generalizes across varying team sizes and task scenarios. Furthermore, multi-group hardware experiments show that the same policy can safely operate in dynamic environments, where other drone teams act as moving obstacles. These results indicate that the proposed framework enables efficient, safe, and scalable multi-drone payload transportation with strong generalization to complex real-world conditions.
We propose a novel framework that computes the corrective control efforts to ensure joint safety in multi-agent dynamical systems. This framework efficiently distributes the required corrective effort without revealing individual agents' private preferences. Our framework integrates high-order control barrier functions (HOCBFs), which enforce safety constraints with formal guarantees of safety for complex dynamical systems, with a privacy-preserving resource allocation mechanism based on the progressive second price (PSP) auction. When a joint safety constraint is violated, agents iteratively bid on new corrective efforts via 'avoidance credits' rather than explicitly solving for feasible corrective efforts that remove the safety violation. The resulting correction, determined via a second price payment rule, coincides with the socially optimal safe distribution of corrective actions. Critically, the bidding process achieves this optimal allocation efficiently and without revealing private preferences of individual agents. We demonstrate this method through multi-robot hardware experiments on the Robotarium platform.
This work addresses the challenge of safe and efficient mobile robot navigation in complex dynamic environments with concave moving obstacles. Reactive safe controllers like Control Barrier Functions (CBFs) design obstacle avoidance strategies based only on the current states of the obstacles, risking future collisions. To alleviate this problem, we use Gaussian processes to learn barrier functions online from multimodal motion predictions of obstacles generated by neural networks trained with energy-based learning. The learned barrier functions are then fed into quadratic programs using modulated CBFs (MCBFs), a local-minimum-free version of CBFs, to achieve safe and efficient navigation. The proposed framework makes two key contributions. First, it develops a prediction-to-barrier function online learning pipeline. Second, it introduces an autonomous parameter tuning algorithm that adapts MCBFs to deforming, prediction-based barrier functions. The framework is evaluated in both simulations and real-world experiments, consistently outperforming baselines and demonstrating superior safety and efficiency in crowded dynamic environments.
Learning from Demonstration (LfD) enables intuitive robot skill acquisition by allowing robots to learn directly from human task demonstrations. However, current methods often fail to address the fact that due to suboptimal and inconsistent human behavior, the quality of the demonstration can vary within each demonstration. Therefore, we introduce LOPAL (LOcal Performance-aware Active Learning), an active learning approach that leverages this local demonstration quality information. Our approach consists of two synergistic components. First, a local performance-driven LfD method uses a Gaussian Mixture Model (GMM) to encode both the demonstrated trajectories and their associated local quality assessments. This enables the generation of trajectories that outperform the imperfect demonstrations by utilizing complementary local data of high performance. Second, active data acquisition allows to improve beyond the imperfect demonstrations by collecting additional informative samples. In areas missing good data, the user is actively requested to provide corrections through a shared autonomy (SA) mechanism, while the robot autonomously executes the learned behavior. The efficacy of LOPAL was validated in both a simulation and a real-world experiment. The results from a real-world pipe inspection task showed that the proposed approach can achieve up to 27.31 % improvement in task performance while also reducing the effort required to collect the demonstrations.
Dynamic obstacle avoidance (DOA) for unmanned aerial vehicles (UAVs) requires fast reaction under limited onboard resources. We introduce the distributionally robust acceleration control barrier function (DR-ACBF) as an efficient collision avoidance method maintaining safety regions. The method constructs a second-order control barrier function as linear half-space constraints on commanded acceleration. Latency, actuator limits, and obstacle accelerations are handled through an effective clearance that considers dynamics and delay. Uncertainty is mitigated using Cantelli tightening with per-obstacle risk. A DR-conditional value at risk (DR-CVaR)based early trigger expands margins near violations to improve DOA. Real-time execution is ensured via constant-time Gauss-Southwell projections. Simulation studies achieve similar avoidance performance at substantially lower computational effort than state-of-the-art baseline approaches. Experiments with Crazyflie drones demonstrate the feasibility of our approach.
Control barrier functions (CBFs) are an effective model-based tool to formally certify the safety of a system. With the growing complexity of modern control problems, CBFs have received increasing attention in both optimization-based and learning-based control communities as a safety filter, owing to their provable guarantees. However, success in transferring these guarantees to real-world systems is critically tied to model accuracy. For example, payloads or wind disturbances can significantly influence the dynamics of an aerial vehicle and invalidate the safety guarantee. In this work, we propose an efficient yet flexible online learning-enhanced high-order adaptive control barrier function using Neural ODEs. Our approach improves the safety of a CBF controller on the fly, even under complex time-varying model perturbations. In particular, we deploy our hybrid adaptive CBF controller on a 38g nano quadrotor, keeping a safe distance from the obstacle, against 18km/h wind.
High-risk applications in robotics, such as robot-assisted surgery, present unique challenges. These systems must be both highly precise and interpretable in order to be deployed in environments with very low tolerance for error or unsafe exploration. We present the first robotic system to demonstrate autonomous clip positioning on a physical phantom in laparoscopic surgery, one of the most common interventions in general surgery. After segmentation of a colorless point cloud from a single camera, target positions for the clips are extracted using spline interpolation, and can then be adjusted by the human operator. The segmentation model is trained on only 60 hand-labeled real point clouds, reflecting data scarcity in the surgical domain. We overcome this with a combination of pre-training on 128,000 synthetic point clouds and two novel data augmentation techniques. The motion of the end-effector to each target is visualized for the operator, satisfying the unique motion constraints of minimally-invasive surgery while ensuring that the robot's actions are verifiable and interpretable. In real robot experiments, our system localizes targets with the required precision of 0.75mm at a 95% success rate and executes autonomous clip positioning with a 100% success rate. We provide insights that are applicable to many other surgical and non-surgical tasks that require identifying and navigating to a precise target. Source code and project page: https://github.com/balazsgyenes/kirurc
Recent advancements in legged robot locomotion have facilitated traversal over increasingly complex terrains. Despite this progress, many existing approaches rely on end-to-end deep reinforcement learning (DRL), which poses limitations in terms of safety and interpretability, especially when generalizing to novel terrains. To overcome these challenges, we introduce VOCALoco, a modular skill-selection framework that dynamically adapts locomotion strategies based on perceptual input. Given a set of pre-trained locomotion policies, VOCALoco evaluates their viability and energy-consumption by predicting both the safety of execution and the anticipated cost of transport over a fixed planning horizon. This joint assessment enables the selection of policies that are both safe and energy-efficient, given the observed local terrain. We evaluate our approach on staircase locomotion tasks, demonstrating its performance in both simulated and real-world scenarios using a quadrupedal robot. Empirical results show that VOCALoco achieves improved robustness and safety during stair ascent and descent compared to a conventional end-to-end DRL policy
Reliable navigation in unstructured, real-world environments remains a significant challenge for embodied agents, especially when operating across diverse terrains, weather conditions, and sensor configurations. In this paper, we introduce GeNIE (Generalizable Navigation System for In-the-Wild Environments), a robust navigation framework designed for global deployment. GeNIE integrates a generalizable traversability prediction model built on SAM2 with a novel path fusion strategy that enhances planning stability in noisy and ambiguous settings. We deployed GeNIE in the Earth Rover Challenge (ERC) at ICRA 2025, where it was evaluated across six countries spanning three continents. GeNIE took first place and achieved 79% of the maximum possible score, outperforming the second-best team by 17%, and completed the entire competition without a single human intervention. These results set a new benchmark for robust, generalizable outdoor robot navigation. We will release the codebase, pretrained model weights, and newly curated datasets to support future research in real-world navigation.
In autonomous driving, place recognition is critical for global localization in GPS-denied environments. LiDAR and radar-based place recognition methods have garnered increasing attention, as LiDAR provides precise ranging, whereas radar excels in adverse weather resilience. However, effectively leveraging LiDAR-radar fusion for place recognition remains challenging. The noisy and sparse nature of radar data limits its potential to further improve recognition accuracy. In addition, heterogeneous radar configurations complicate the development of unified cross-modality fusion frameworks. In this paper, we propose LRFusionPR, which improves recognition accuracy and robustness by fusing LiDAR with either single-chip or scanning radar. Technically, a dual-branch network is proposed to fuse different modalities within the unified polar coordinate bird's eye view (BEV) representation. In the fusion branch, cross-attention is utilized to perform cross-modality feature interactions. The knowledge from the fusion branch is simultaneously transferred to the distillation branch, which takes radar as its only input to further improve the robustness. Ultimately, the descriptors from both branches are concatenated, producing the multimodal global descriptor for place retrieval. Extensive evaluations on multiple datasets demonstrate that our LRFusionPR achieves accurate place recognition, while maintaining robustness under varying weather conditions. Our open-source code will be released at https://github.com/QiZS-BIT/LRFusionPR.
Navigating unknown environments to find a target object is a significant challenge. While semantic information is crucial for navigation, relying solely on it for decision-making may not always be efficient, especially in environments with weak semantic cues. Additionally, many methods are susceptible to misdetections, especially in environments with visually similar objects. To address these limitations, we propose ApexNav, a zero-shot object navigation framework that is both more efficient and reliable. For efficiency, ApexNav adaptively utilizes semantic information by analyzing its distribution in the environment, guiding exploration through semantic reasoning when cues are strong, and switching to geometry-based exploration when they are weak. For reliability, we propose a target-centric semantic fusion method that preserves long-term memory of the target and similar objects, enabling robust object identification even under noisy detections. We evaluate ApexNav on the HM3Dv1, HM3Dv2, and MP3D datasets, where it outperforms state-of-the-art methods in both SR and SPL metrics. Comprehensive ablation studies further demonstrate the effectiveness of each module. Furthermore, real-world experiments validate the practicality of ApexNav in physical environments. The code will be released at https://github.com/Robotics-STAR-Lab/ApexNav.
Cutting-edge robot learning techniques including foundation models and imitation learning from humans all pose huge demands on large-scale and high-quality datasets which constitute one of the bottleneck in the general intelligent robot fields. This paper presents the Kaiwu multimodal dataset to address the missing real-world synchronized multimodal data problems in the sophisticated assembling scenario,especially with dynamics information and its fine-grained labelling. The dataset first provides an integration of human,environment and robot data collection framework with 20 subjects and 30 interaction objects resulting in totally 11,664 instances of integrated actions. For each of the demonstration,hand motions,operation pressures,sounds of the assembling process,multi-view videos, high-precision motion capture information,eye gaze with first-person videos,electromyography signals are all recorded. Fine-grained multi-level annotation based on absolute timestamp,and semantic segmentation labelling are performed. Kaiwu dataset aims to facilitate robot learning,dexterous manipulation,human intention investigation and human-robot collaboration research.
Recently, Vision-Language-Action models (VLA) have advanced robot imitation learning, but high data collection costs and limited demonstrations hinder generalization and current imitation learning methods struggle in out-of-distribution scenarios, especially for long-horizon tasks. A key challenge is how to mitigate compounding errors in imitation learning, which lead to cascading failures over extended trajectories. To address these challenges, we propose the Diffusion Trajectory-guided Policy (DTP) framework, which generates 2D trajectories through a diffusion model to guide policy learning for long-horizon tasks. By leveraging task-relevant trajectories, DTP provides trajectory-level guidance to reduce error accumulation. Our two-stage approach first trains a generative vision-language model to create diffusion-based trajectories, then refines the imitation policy using them. Experiments on the CALVIN benchmark show that DTP outperforms state-of-the-art baselines by 25% in success rate, starting from scratch without external pretraining. Moreover, DTP significantly improves real-world robot performance.
The cooperation of a pair of robot manipulators is required to manipulate a target object without any fixtures. The conventional control methods coordinate the end-effector pose of each manipulator with that of the other using their kinematics and joint coordinate measurements. Yet, the manipulators' inaccurate kinematics and joint coordinate measurements can cause significant pose synchronization errors in practice. This paper thus proposes an image-based visual servoing approach for enhancing the cooperation of a dual-arm manipulation system. On top of the classical control, the visual servoing controller lets each manipulator use its carried camera to measure the image features of the other's marker and adapt its end-effector pose with the counterpart on the move. Because visual measurements are robust to kinematic errors, the proposed control can reduce the end-effector pose synchronization errors and the fluctuations of the interaction forces of the pair of manipulators on the move. Theoretical analyses have rigorously proven the stability of the closed-loop system. Comparative experiments on real robots have substantiated the effectiveness of the proposed control.
Sampling-based motion planners (SBMPs) are effective for planning with complex kinodynamic constraints in high-dimensional spaces, but they still struggle to achieve real-time performance, which is mainly due to their serial computation design. We present Kinodynamic Parallel Accelerated eXpansion (Kino-PAX), a novel highly parallel kinodynamic SBMP designed for parallel devices such as GPUs. Kino-PAX grows a tree of trajectory segments directly in parallel. Our key insight is how to decompose the iterative tree growth process into three massively parallel subroutines. Kino-PAX is designed to align with the parallel device execution hierarchies, through ensuring that threads are largely independent, share equal workloads, and take advantage of low-latency resources while minimizing high-latency data transfers and process synchronization. This design results in a very efficient GPU implementation. We prove that Kino-PAX is probabilistically complete and analyze its scalability with compute hardware improvements. Empirical evaluations demonstrate solutions in the order of 10 ms on a desktop GPU and in the order of 100 ms on an embedded GPU, representing up to 1000 times improvement compared to coarse-grained CPU parallelization of state-of-the-art sequential algorithms over a range of complex environments and systems.
Agile flight in complex environments poses significant challenges to current motion planning methods, as they often fail to fully leverage the quadrotor dynamic potential, leading to performance failures and reduced efficiency during aggressive maneuvers.Existing approaches frequently decouple trajectory optimization from control generation and neglect the dynamics, further limiting their ability to generate aggressive and feasible motions.To address these challenges, we introduce an enhanced Search-to-Control planning framework that integrates visibility path searching with reinforcement learning (RL) control generation, directly accounting for dynamics and bridging the gap between planning and control.Our method first extracts control points from collision-free paths using a proposed heuristic search, which are then refined by an RL policy to generate low-level control commands for the quadrotor controller, utilizing reduced-dimensional obstacle observations for efficient inference with lightweight neural networks.We validate the framework through simulations and real-world experiments, demonstrating improved time efficiency and dynamic maneuverability compared to existing methods, while confirming its robustness and applicability.